Galaxy structural properties such as size, morphology, and surface brightness bear the imprint of galaxies' evolutionary histories, and so are related with other properties such as stellar mass, star formation rate, and emergent spectra. In this dissertation, I present three studies exploring such relationships. In the first, I investigated the relationships between 4000 Å break (D4000) strength, colors, stellar masses, and morphology in a sample of 352 galaxies at intermediate redshifts based on photometric and spectroscopic data from the Hubble Space Telescope (HST). I explored several diagrams such as UVJ color space combined with the D4000 strengths and the structural parameters of sample galaxies. The analysis shows that the presence of a bulge component is a necessary but not sufficient requirement for star formation quenching at intermediate redshifts. In the second study, I investigated the central 250 pc UV star formation intensity (SFI, star formation rate per unit area) of a sample of 40 Green Pea (GP) galaxies and 15 local Lyman Break Galaxy Analogs (LBAs) to understand the Lyα escape mechanisms and the associations with the SFI in Lyα-emitters (LAEs). I utilized the Cosmic Origins Spectrograph near-ultraviolet (COS/NUV) images from the HST. I found that the Lyα equivalent width (EW(Lyα)) and the Lyα escape fraction are positively correlated with the ratio of SFI to galaxy stellar mass. These correlations suggest the importance of the central SFI in Lyα photon escape. In the third study, I investigated the UV photometric properties of a sample of 40 GPs and the possible associations with Lyα escape mechanisms. I measured the UV-continuum size and luminosity of the sample galaxies by employing the COS/NUV images. The circularized half-light radius of GPs shows compact sizes and it further shows the statistically significant anti-correlations with EW(Lyα) and the Lyα escape fraction. The size comparison of GPs to those of high-redshift LAEs shows that their sizes are similar, once spatial resolution effects are properly considered. These results show that a compact size is crucial for escape of Lyα photons, and that Lyα emitters show constant characteristic size independent of their redshift. Therefore, the results presented in this dissertation emphasize the importance of galaxy structural properties in star formation quenching and in Lyα escape.

Green pea galaxies are a class of rare, compact starburst galaxies that have powerful optical emission line [OIII]$\lambda$5007. They are the best low-redshift analogs of high-redshift (z$>$2) Lyman-alpha emitting galaxies (LAEs). They provide unique opportunities to study physical conditions in high-redshift LAEs in great detail. In this dissertation, a few physical properties of green peas are investigated. The first study in the dissertation presents star formation rate (SFR) surface density, thermal pressure in HII regions, and a correlation between them for 17 green peas and 19 Lyman break analogs, which are nearby analogs of high-redshift Lyman break galaxies. This correlation is consistent with that found from the star-forming galaxies at z $\sim$ 2.5. In the second study, a new large sample of 835 green peas in the redshift range z = 0.011 -- 0.411 are assembled from Data Release 13 of the Sloan Digital Sky Survey (SDSS) with the equivalent width of the line [OIII]$\lambda$5007 $>$ 300\AA\ or the equivalent width of the line H$\beta$ $>$ 100\AA. The size of this new sample is ten times that of the original 80 star-forming green pea sample. With reliable T$_e$-based gas-phase metallicity measurements for the 835 green peas, a new empirical calibration of R23 (defined as ([OIII]$\lambda$$\lambda$4959,5007 + [OII]$\lambda$$\lambda$3726,3729)/H$\beta$) for strong line emitters is then derived. The double-value degeneracy of the metallicity is broken for galaxies with large ionization parameter (which manifests as log([OIII]$\lambda$$\lambda$4959,5007/[OII]$\lambda$$\lambda$3726,3729) $\geq$ 0.6). This calibration offers a good way to estimate metallicities for extreme emission-line galaxies and high-redshift LAEs. The third study presents stellar mass measurements and the stellar mass-metallicity relation of 828 green peas from the second study. The stellar mass covers 6 orders of magnitude in the range 10$^{5}$ -- 10$^{11}$ M$_{\odot}$, with a median value of 10$^{8.8}$ M$_{\odot}$. The stellar mass-metallicity relation of green peas is flatter and displays about 0.2 - 0.5 dex offset to lower metallicities in the range of stellar mass higher than 10$^{8}$ M$_{\odot}$ compared to the local SDSS star-forming galaxies. A significant dependence of the stellar mass-metallicity relation on star formation rate is not found in this work.

In the past three decades with the deployment of space-based from x-rays to infrared telescopes and operation of 8-10 m class ground based telescopes, a hand-full of regions of the sky have emerged that probe the distant universe over relatively wide fields with the aim of understanding the assembly of apparently faint galaxies. To explore this new frontier, observations were made with the Large Binocular Cameras (LBCs) on the Large Binocular Telescope (LBT) of a well-studied deep field, GOODS-North, which has been observed by a wide range of telescopes from the radio to x-ray. I present a study of the trade-off between depth and resolution using a large number of LBT/LBC U-band and R-band imaging observations in the GOODS-N field. Having acquired over 30 hours of data (315 images with 5-6 minute exposures) for U-band and 27 hours for R-band (828 images with 2 minute exposures), multiple mosaics were generated, starting with images taken under the best atmospheric conditions (FWHM <0.8"). For subsequent mosaics, data with coarser seeing values were added in until the final, deepest mosaic included all images with FWHM <1.8". For each mosaic, object catalogs were made to compare the optimal-resolution, yet shallower image to the low-resolution but deeper image. For the brightest galaxies within the GOODS-N field, structure and clumpy features within the galaxies are more prominent in the optimal-resolution image compared to the deeper mosaics. I conclude that for studies of brighter galaxies and features within them, the optimal-resolution image should be used. However, to fully explore and understand the faintest objects, the deeper imaging with lower resolution are also required. For the 220 and 360 brightest galaxies in the U-band and R-band images respectively, there is only a marginal difference between the optimal-resolution and lower-resolution light-profiles and their integrated total fluxes. This helps constrain how much flux can be missed in galaxy outskirts, which is important for studies of Extragalactic Background Light. Finally, I also comment on a collection of galaxies in the field with tidal tails and streams, diffuse plumes, and bridges.

High-energy explosive phenomena, Gamma-Ray Bursts (GRBs) and Supernovae (SNe), provide unique laboratories to study extreme physics and potentially open up the new discovery window of Gravitational-wave astronomy.

Uncovering the intrinsic variability of GRBs constrains the size of the GRB emission region, and ejecta velocity, in turn provides hints on the nature of GRBs and their progenitors. We develop a novel method which ties together wavelet and structure-function analyses to measure, for the first time, the actual minimum variability timescale, Delta t_min, of GRB light curves. Implementing our technique to the largest sample of GRBs collected by Swift and Fermi instruments reveals that only less than 10% of GRBs exhibit evidence for variability on timescales below 2 ms. Investigation on various energy bands of the Gamma-ray Burst Monitor (GBM) onboard Fermi shows that the tightest constraints on progenitor radii derive from timescales obtained from the hardest energy channel of light curves (299--1000 keV). Our derivations for the minimum Lorentz factor, Gamma_min, and the minimum emission radius, R = 2c Gamma_min^2 Delta t_min / (1+z), find Gamma < 400 which imply typical emission radii R ~ 1 X 10^14 cm for long-duration GRBs and R ~ 3 X 10^13 cm for short-duration GRBs (sGRBs).

I present the Reionization and Transients InfraRed (RATIR) followup of LIGO/Virgo Gravitational-wave events especially for the G194575 trigger. I show that expanding our pipeline to search for either optical riZ or near-infrared YJH detections (3 or more bands)

should result in a false-alarm-rate ~1% (one candidate in the vast 100 deg^2 LIGO error region) and an efficiency ~90%.

I also present the results of a 5-year comprehensive SN search by the Palomar Transient Factory aimed to measure the SN rates in the local Luminous Infrared Galaxies. We find that the SN rate of the sample, 0.05 +/- 0.02 1/yr (per galaxy), is consistent with that expected from the theoretical prediction, 0.060 +/- 0.002 1/yr (per galaxy).

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.

Understanding the properties and formation histories of individual stars in galaxies remains one of the most important areas in astrophysics. The impact of the Hubble Space Telescope<\italic> (HST<\italic>) has been revolutionary, providing deep observations of nearby galaxies at high resolution and unprecedented sensitivity over a wavelength range from near-ultraviolet to near-infrared. In this study, I use deep HST<\italic> imaging observations of three nearby star-forming galaxies (M83, NGC 4214, and CGCG 269-049) based on the HST<\italic> observations, in order to provide to construct color-magnitude and color-color diagrams of their resolved stellar populations. First, I select 50 regions in the spiral arm and inter-arm areas of M83, and determine the age distribution of the luminous stellar populations in each region. I developed an innovative method of star-by-star correction for internal extinction to improve stellar age and mass estimates. I compare the extinction-corrected ages of the 50 regions with those determined from several independent methods. The young stars are much more likely to be found in concentrated aggregates along spiral arms, while older stars are more dispersed. These results are consistent with a scenario where star formation is associated with the spiral arms, and stars form primarily in star clusters before dispersing on short timescales to form the field population. I address the effects of spatial resolution on the measured colors, magnitudes, and age estimates. While individual stars can occasionally show measurable differences in the colors and magnitudes, the age estimates for entire regions are only slightly affected. The same procedure is applied to nearby starbursting dwarf NGC 4214 to study the distributions of young and old stellar populations. Lastly, I describe the analysis of the HST<\italic> and Spitzer Space Telescope<\italic> observations of the extremely metal-poor dwarf galaxy (XMPG) CGCG 269-049 at a distance of 4.96 Mpc. This galaxy is one of the most metal-poor known with 12+log(O/H)=7.43. I find clear evidence for the presence of an old stellar population in CGCG~269-049, ruling out the possibility that this galaxy is forming its first generation of stars, as originally proposed for XMPGs. This comprehensive study of resolved stellar populations in three nearby galaxies provides detailed view of the current state of star formation and evolution of galaxies.