Learning how properties of galaxies such as star formation, galaxy interactions, chemical composition, and others evolve to produce the modern universe has long been a goal of extragalactic astronomy. In recent years, grism spectroscopy from the Hubble Space Telescope (HST) has provided a means to study these properties with spectroscopy while avoiding the limitations of ground-based observation. In this dissertation, I present several studies wherein I used HST G102 grism spectroscopy from the Faint Infrared Grism Survey (FIGS) to investigate these fundamental properties of galaxies and how they interact and evolve. In the first study, I combined the grism spectra with broadband photometry to produce a catalog of redshifts with improved accuracy, reducing the median redshift error from 3\% to 2\%. With this redshift catalog, I conducted a systematic search for galaxy overdensities in the FIGS fields, producing a list of 24 significant candidates. In the second study, I developed a method for identifying emission line galaxy (ELG) candidates from continuum-subtracted 1D spectra, and identified 71 ELGs in one FIGS field. In matching MUSE/VLT spectra, I measured the [OIII]$\lambda$4363 emission line for 14 FIGS ELGs, and used this to measure their $T_e$-based gas-phase metallicities. These ELGs show a low-metallicity offset on the Mass-Metallicity Relation, and I demonstrated that this offset can be explained by recent star formation. In the third study, I expanded the ELG search to all four FIGS fields, identifying 208 H$\alpha$, [OIII]$\lambda\lambda$4959,5007, and [OII]$\lambda\lambda$3727,3729 line emitters. I compiled a catalog of line fluxes, redshifts, and equivalent widths. I combined this catalog with the overdensity study to investigate a possible relationship between line luminosity, star formation, and an ELG's environment. In the fourth study, I usde 15 FIGS H$\alpha$ emitters and 49 ``green pea'' line emitters to compare H$\alpha$ and the far-UV continuum as tracers of star formation. I explored a correlation between the H$\alpha$-FUV ratio and the ratio of [OIII]$\lambda\lambda$4959,5007 to [OII]$\lambda\lambda$3727,3729 and its implications for star formation history.

I combine, compare, and contrast the results from two different numerical techniques (grid vs. particle methods) studying multi-scale processes in galaxy and structure formation. I produce a method for recreating identical initial conditions for one method from those of the other, and explore methodologies necessary for making these two methods as consistent as possible. With this, I first study the impact of streaming velocities of baryons with respect to dark matter, present at the epoch of reionization, on the ability for small halos to accrete gas at high redshift. With the inclusion of this stream velocity, I find the central density profile of halos is reduced, overall gas condensation is delayed, and infer a delay in the inevitable creation of stars.

I then combine the two numerical methods to study starburst outflows as they interact with satellite halos. This process leads to shocks catalyzing the formation of molecular coolants that lead to bursts in star formation, a process that is better captured in grid methods. The resultant clumps of stars are removed from their initial dark matter halo, resemble precursors to modern-day globular clusters, and their formation may be observable with upcoming telescopes.

Finally, I perform two simulation suites, comparing each numerical method's ability to model the impact of energetic feedback from accreting black holes at the core of giant clusters. With these comparisons I show that black hole feedback can maintain a hot diffuse medium while limiting the amount of gas that can condense into the interstellar medium, reducing the central star formation by up to an order of magnitude.

Quasars, the visible phenomena associated with the active accretion phase of super- massive black holes found in the centers of galaxies, represent one of the most energetic processes in the Universe. As matter falls into the central black hole, it is accelerated and collisionally heated, and the radiation emitted can outshine the combined light of all the stars in the host galaxy. Studies of quasar host galaxies at ultraviolet to near-infrared wavelengths are fundamentally limited by the precision with which the light from the central quasar accretion can be disentangled from the light of stars in the surrounding host galaxy. In this Dissertation, I discuss direct imaging of quasar host galaxies at redshifts z ≃ 2 and z ≃ 6 using new data obtained with the Hubble Space Telescope. I describe a new method for removing the point source flux using Markov Chain Monte Carlo parameter estimation and simultaneous modeling of the point source and host galaxy. I then discuss applications of this method to understanding the physical properties of high-redshift quasar host galaxies including their structures, luminosities, sizes, and colors, and inferred stellar population properties such as age, mass, and dust content.

Lyman-alpha (Lyα) galaxies (LAEs) and Lyα blobs (LABs) are objects identified and studied due to their bright Lyα emission lines. This bright emission allows LAEs and LABs to be studied in the distant universe, providing a glimpse into the physical processes occuring in the early universe. This dissertation presents three complementary studies of LAEs and LABs at z ~ 3.1. The two main foci of this work are (1) to understand the gas kinematics in both classes of objects and (2) to improve spectral energy distribution (SED) fitting processes to better determine the physical characteristics of LAEs. Gas kinematics in this dissertation means looking for signatures of large-scale winds. This is an exciting astrophysical endeavor, because the results can provide insight into how Lyα photons escape distant galaxies and traverse the IGM, and the results have implications for how the epoch of reionization can be studied with the Lyα line and because winds can be a signature of powerful star formation events. In the first two studies we find signatures of winds in three LAEs by measuring the velocity offset between the redshifts of [OIII] and Lyα in these galaxies. The first two LAEs presented here represent the first ever measurements of [OIII] in Lyα-selected field galaxies. The third study reports no velocity offset between [OIII] and Lyα when the methodology is transferred to a z ~ 3.1 LAB. This lack of velocity offset is an interesting result, however, as powerful outflows and star formation events, which should impart a velocity offset, have been hypothesized as power sources for LABs. In addition to understanding the kinematics of these objects, we introduce a new parameter into the SED fitting process typically used to characterize LAEs. This new parameter enables better determination of characteristics like the age, mass, metallicity, dust content and star formation history of the galaxies in our sample. These characteristics provide a snapshot of galaxies in the universe ~ 11 billion years ago and also provide insight into how these characteristics compare to galaxies at other epochs.

Numerical simulations are very helpful in understanding the physics of the formation of structure and galaxies. However, it is sometimes difficult to interpret model data with respect to observations, partly due to the difficulties and background noise inherent to observation. The goal, here, is to attempt to bridge this gap between simulation and observation by rendering the model output in image format which is then processed by tools commonly used in observational astronomy. Images are synthesized in various filters by folding the output of cosmological simulations of gasdynamics with star-formation and dark matter with the Bruzual- Charlot stellar population synthesis models. A variation of the Virgo-Gadget numerical simulation code is used with the hybrid gas and stellar formation models of Springel and Hernquist (2003). Outputs taken at various redshifts are stacked to create a synthetic view of the simulated star clusters. Source Extractor (SExtractor) is used to find groupings of stellar populations which are considered as galaxies or galaxy building blocks and photometry used to estimate the rest frame luminosities and distribution functions. With further refinements, this is expected to provide support for missions such as JWST, as well as to probe what additional physics are needed to model the data. The results show good agreement in many respects with observed properties of the galaxy luminosity function (LF) over a wide range of high redshifts. In particular, the slope (alpha) when fitted to the standard Schechter function shows excellent agreement both in value and evolution with redshift, when compared with observation. Discrepancies of other properties with observation are seen to be a result of limitations of the simulation and additional feedback mechanisms which are needed.

The first part of this dissertation presents the implementation of Bayesian statistics with galaxy surface luminosity (SL) prior probabilities to improve the ac- curacy of photometric redshifts. The addition of the SL prior probability helps break the degeneracy of spectro-photometric redshifts (SPZs) between low redshift 4000 A break galaxies and high redshift Lyman break galaxies which are mostly catas- trophic outliers. For a sample of 1138 galaxies with spectroscopic redshifts in the GOODS North and South fields at z < 1.6, the application of the surface luminosity prior reduces the fraction of galaxies with redshift deviation sigma(z) > 0.2 from 15.0% to 10.4%. The second part of this dissertation presents the study of the chemical evolution of the star-forming galaxies. The Hubble Space Telescope Probing Evolution and Reionization Spectroscopically (PEARS) grism Survey effectively selects emission line galaxies (ELGs) to mAB ~ 27. Follow-up Magellan LDSS3+IMACS spectroscopy of the HST/ACS PEARS ELGs confirms an accuracy of sigma_z = 0.006 for the HST/ACS PEARS grism redshifts. The luminosity-metallicity (L-Z) relation and the mass-metallicity (M-Z) relation of the PEARS ELGs at z ~ 0.6 are offset by ~ - 0.8 dex in metallicity for a given rest-frame B absolute magnitude and stellar mass relative to the local relations from SDSS galaxies. The offsets in both relations are ~ - 0.4 dex larger than that given by other samples at same redshifts, which are demonstrated to be due to the selection of different physical properties of the PEARS ELGs: low metallicities, very blue colors, small sizes, compact disturbed morphologies, high SSFR > 10^-9 yr^-1 , and high gas fraction. The downsizing effect, the tidal interacting induced inflow of metal-poor gas, and the SNe driven galactic winds outflows, may account for the significant offset of the PEARS galaxies in the L-Z and the M-Z relations relative to the local relations. The detection of the emission lines of ELGs down to m ~ 26 mag in the HST/ACS PEARS + HST/WCF3 ERS NIR composit grism spectra enables to extend the study of the evolution of the L-Z and M-Z relations to 0.6 < z < 2.4.

Galaxies with strong Lyman-alpha (Lya) emission line (also called Lya galaxies or emitters) offer an unique probe of the epoch of reionization - one of the important phases when most of the neutral hydrogen in the universe was ionized. In addition, Lya galaxies at high redshifts are a powerful tool to study low-mass galaxy formation. Since current observations suggest that the reionization is complete by redshift z~ 6, it is therefore necessary to discover galaxies at z > 6, to use their luminosity function (LF) as a probe of reionization. I found five z = 7.7 candidate Lya galaxies with line fluxes > 7x10-18 erg/s/cm/2 , from three different deep near-infrared (IR) narrowband (NB) imaging surveys in a volume > 4x104Mpc3. From the spectroscopic followup of four candidate galaxies, and with the current spectroscopic sensitivity, the detection of only the brightest candidate galaxy can be ruled out at 5 sigma level. Moreover, these observations successfully demonstrate that the sensitivity necessary for both, the NB imaging as well as the spectroscopic followup of z~ 8 Lya galaxies can be reached with the current instrumentation. While future, more sensitive spectroscopic observations are necessary, the observed Lya LF at z = 7.7 is consistent with z = 6.6 LF, suggesting that the intergalactic medium (IGM) is relatively ionized even at z = 7.7, with neutral fraction xHI≤ 30%. On the theoretical front, while several models of Lya emitters have been developed, the physical nature of Lya emitters is not yet completely known. Moreover, multi-parameter models and their complexities necessitates a simpler model. I have developed a simple, single-parameter model to populate dark mater halos with Lya emitters. The central tenet of this model, different from many of the earlier models, is that the star-formation rate (SFR), and hence the Lya luminosity, is proportional to the mass accretion rate rather than the total halo mass. This simple model is successful in reproducing many observable including LFs, stellar masses, SFRs, and clustering of Lya emitters from z~ 3 to z~ 7. Finally, using this model, I find that the mass accretion, and hence the star-formation in > 30% of Lya emitters at z~ 3 occur through major mergers, and this fraction increases to ~ 50% at z~7.

Type Ia supernovae are important, but mysterious cosmological tools. Their standard brightnesses have enabled cosmologists to measure extreme distances and to discover dark energy. However, the nature of their progenitor mechanisms remains elusive, with many competing models offering only partial clues to their origins. Here, type Ia supernova delay times are explored using analytical models. Combined with a new observation technique, this model places new constraints on the characteristic time delay between the formation of stars and the first type Ia supernovae. This derived delay time (500 million years) implies low-mass companions for single degenerate progenitor scenarios. In the latter portions of this dissertation, two progenitor mechanisms are simulated in detail; white dwarf collisions and mergers. From the first of these simulations, it is evident that white dwarf collisions offer a viable and unique pathway to producing type Ia supernovae. Many of the combinations of masses simulated produce sufficient quantities of 56Ni (up to 0.51 solar masses) to masquerade as normal type Ia supernovae. Other combinations of masses produce 56Ni yields that span the entire range of supernova brightnesses, from the very dim and underluminous, with 0.14 solar masses, to the over-bright and superluminous, with up to 1.71 solar masses. The 56Ni yield in the collision simulations depends non-linearly on total system mass, mass ratio, and impact parameter. Using the same numerical tools as in the collisions examination, white dwarf mergers are studied in detail. Nearly all of the simulations produce merger remnants consisting of a cold, degenerate core surrounded by a hot accretion disk. The properties of these disks have strong implications for various viscosity treatments that have attempted to pin down the accretion times. Some mass combinations produce super-Chandrasekhar cores on shorter time scales than viscosity driven accretion. A handful of simulations also exhibit helium detonations on the surface of the primary that bear a resemblance to helium novae. Finally, some of the preliminary groundwork that has been laid for constructing a new numerical tool is discussed. This new tool advances the merger simulations further than any research group has done before, and has the potential to answer some of the lingering questions that the merger study has uncovered. The results of thermal diffusion tests using this tool have a remarkable correspondence to analytical predictions.

Gamma-ray burst observations provide a great opportunity for cosmography in high redshift. Some tight correlations between different physical properties of GRBs are discovered and used for cosmography. However, data selection, assumptions, systematic uncertainty and some other issues affect most of them. Most importantly, until the physical origin of a relation is understood, one should be cautious to employ the relation to utilize Gamma ray bursts for cosmography. In the first part of this dissertation, I use Liang-Zhang correlation to constrain ¦« Cold Dark Matter standard cosmology and a particular class of brane cosmology (brane-induced gravity model). With the most probable model being ¦¸_m=0.23 and ¦¸_¦«=0.77 for flat ¦«CDM cosmology and ¦¸_m=0.18 and ¦¸_(r_c )=0.17 for flat brane-induced gravity cosmology, my result for the energy components of these two models is comparable with the result from SNIa observation. With average uncertainty of distance modulus being 0.2771, the two discussed cosmologies are indistinguishable using my current sample of GRB with redshift ranging between 0.1685 and 3.2. I argue that by expanding my sample and adding more low and high redshift GRBs and also with improvement in using GRB for cosmography, we might be able to distinguish between different cosmological models and tighten the most probable model. Looking into correlation and evolution of GRB prompt emission and afterglow has many advantages. It helps to open windows to comprehend the physics of GRBs and examine different GRB models. It is also possible to use GRB correlation as an accurate redshift estimator and more importantly to constrain the cosmological parameters. XRT flares of GRB afterglow are thought to be the result of central engine activity. Studying this component leads us to understand GRB flare and central engine nature. In the next part of this dissertation, I study the correlation and evolution of different prompt emission and afterglow GRB properties and some GRB flare-based quantities. Considering instrument bias and selection effect, I conclude some well-correlated correlations and establish some property evolution. The correlation between average luminosity and isotropic ¦Ã-ray energy, energy of plateau and isotropic ¦Ã-ray energy and luminosity at break time and break time and evolution of plateau energy are well established. It is also realized that the apparent evolution of isotropic ¦Ã-ray energy and average luminosity is due to the instrumental flux threshold. With expanding the sample of GRB and accommodating more GRBs with XRT flares to my sample, I can reevaluate my result more firmly and confirm or rule out some hard to assert results due to limited number of data. In search for physically motivated GRB relation, analyzing the thermal component of GRB prompt emission, I derive two well-correlated relations. They are between calculated and estimated flux of the GRB thermal component for the co-moving bolometric and co-moving detector band-pass range of spectrum. In this study, three samples of Swift, pre-Swift and combined samples are used. The quality of this correlation is comparable with the Ghirlanda relation in terms of Spearman rank correlation parameters (correlation coefficient and correlation significance) and reduced ¦Ö^2of best fit. These results for the Swift GRB sample for co-moving bolometric range of spectrum are 0.81, 4.07¡Á¡¼10¡½^(-7) and 0.66 respectively. The derived correlations also imply a E_(¦Ã,iso)-E_peak^4 relation that provides physical insight to E_¦Ã-E_peak Ghirlanda correlation. Three scaling coefficients are employed to study these correlations. Monte Carlo statistics indicates that the existing correlations are independent of these constants. For Swift and combined sample 73% - 84.8% successes are recorded. Therefore, it is expected by determining these constants, the tightness of these correlations will further improve.