This thesis presents studies of cosmic populations of extragalactic radio sources. The problems selected for this thesis are 1) the derivation of constraints on the emergence of new sub-mJy populations at flux density below about 1mJy (at1.4 GHz) paying careful attention to including sources with low surface brightness and counting sources rather than components 2) development of a new method to estimate the asymmetry in the large scale galaxy environment with respect to the axes of extended radio sources and use this to examine for evidence of impact of the environment on the morphology of radio sources. The studies presented herein have been carried out using the Australia Telescope Low Brightness Survey (ATLBS), which is a sensitive radio survey at 1.4 GHz, imaging 8.42 square degrees of the sky along with accompanying optical observations of the same region. There are multiple populations of extragalactic radio sources in the cosmos. These consist of populations of powerful radio-loud quasars and radio galaxies to populations of weaker radio sources such as star-forming galaxies. These populations of radio sources show evidence of evolution with cosmic epoch. Because the radio galaxy phenomenon and the AGNs at the centers of their host galaxies may influence the evolution of the galaxy via feedbacks, examinations of these source populations over cosmic time are a necessary complementary study to understanding the process of galaxy formation and in general, cosmology. Below we give brief introduction to the problems studied in this thesis. Sub-mJy Radio Source Counts Radio source counts, which have historically been a key probe of cosmology, now represent a measure of cosmological evolution in radio source populations. Currently, the estimation of source counts at sub-mJy flux density as well as the nature and evolution of these sources is undetermined. At flux densities ≤1.0 mJy a ‘flattening’ of normalized differential source counts has been widely reported in literature( Windhorst et al.(1985),Hopkins et al.(2003),Huynh et al.(2005) and references therein). The flattening is observed as an apparent change of slope for the normalized differential source counts from ∼0.7 at5.0 −100.0 mJy to about 0.4 in the 0.25 −5.0 mJy range. Attempts to understand the nature of the sub-mJy population have arrived at discordant results and identify the sub-mJy sources with different populations: starburst galaxies(Condon(1989), Benn et al. (1993), Huynhet al. (2005)), early type galaxies (Gruppioniet al., 1999),low(radio) luminosity activegalactic nuclei(AGNs)(Huynh et al.,2008) or a mixture of these. Due to unavailability of spectroscopically complete samples of hosts of sub-mJy sources, the exact nature of the sub-mJy radio source population is currently uncertain. However, the presence of a population which emerges at sub-mJy flux density and is different from the AGN-dominated radio source population is not in doubt. The studies in the literature are inconsistent in identifying the precise location of the emergence of flattening in counts at sub-mJy flux density. Several studies show that the source counts are consistent with a continuation in the slope of the differential counts below mJy flux density (Prandoniet al.(2001) and Subrahmanyan et al.(2010)). The scatter in the sub-mJy counts from different studies may be because of the relatively small areas covered by deep surveys(in many cases, a single pointing of an interferometric array) which may have relatively large errors arising from large scale clustering in the spatial distribution of cosmic radio sources(however the study by Condon (2007) concludes that the scatter in the source counts stems from variations in corrections and sensitivity in different studies)In contrast, wide-field surveys may not reach the depth to probe sub-mJy counts. Another reason is the correction applicable to the observed source counts necessary to estimate the true source counts; these are especially pertinent at low flux densities. To resolve these is-sues, a survey which combines the attributes of wide spatial coverage as well as excellent sensitivity and a procedure which accounts for the biases in estimation of the sub-mJy source counts is needed. In conclusion, accurate measurements of the source counts at sub-mJy flux densities are needed to correctly estimate the cosmic evolution of radio sources. Environments of Extended Radio Sources Another issue of importance in the study of extragalactic radio sources is their interaction with their environments. The gas environments in which radio sources reside and evolve ought to have an influence on the morphology of the radio sources. This has been shown in many case studies where the radio structures have been compared with the X-ray gas environments (Blanton et al. (2011); Boehringer et al.(1993)). Studies of the optical environments of radio galaxies have also been carried out previously (Longair & Seldner, 1979; Yee & Green, 1984; Hill & Lilly, 1991; Zirbel, 1997). The motivation behind these studies has been to examine differences between different classes of radio sources, the evolution of environments with cosmic epoch as well as the possibility of identifying clusters/groups of galaxies using radio sources as a tracer(Wing &Blanton, 2011). Many previous studies have found that the environments of FRI/FRII sources are different and are dependent on the cosmic epoch. FRI sources, typically, are found in rich environments. FRII sources in the local universe are generally hosted by field galaxies, but at higher red shifts are found in richer environments(Hatch et al.,2011;Best et al.,2003;Overzier et al.,2008). However, there have been fewer studies that relate the richness of the environments and morphological asymmetries of radio galaxies. Earlier investigations by Subrahmanyan et al. (2008) and Safouris et al.(2009) are noteworthy in this regard where the radio structures of two giant radio galaxies were examined in the context of the large-scale galaxy distributions in their vicinity(also see Chen et al.(2012) and references therein). The study was also used to infer properties of the ambient thermal gas medium in which the structures evolved. Clear correlations between structural asymmetries and associated extended emission-line gas were also found for radio galaxies that have relatively smaller sizes of a few hundred kpc(McCarthy et al., 1991). Thesis Work To progress the field in the problems highlighted above, the following work has been done in this thesis. Radio Imaging of ATLBS Survey To characterize the cosmic evolution of radio sources and their properties, observations and imaging of faint radio sources is essential. The Australia Telescope Low Brightness Survey(ATLBS), which has been used in the studies presented in this thesis, has been designed specifically to image diffuse radio emission to relatively high red shifts(z ∼1−1.5). Therefore obtaining good surface brightness sensitivity was a prime objective in planning the radio observations and in imaging the data obtained from these observations. This requires a nearly complete synthesized aperture and observations of a representative patch of the extra galactic sky. These requirements have been fulfilled in ATLBS survey, which has excellent uv coverage, especially at short spacings, and images a region off the galactic plane that is devoid of strong radio sources. The observations were carried out for two adjacent fields, designated as A and B with their centers at RA:00h 35m 00s,DEC:−67◦00 00 and RA:00h 59m 17s,DEC:−67◦00 00 ,in the 20 cm band, with a center frequency of1388MHz,infullpolarization mode. The radio data was imaged by using techniques such as multi-frequency deconvolution and self-calibration to make two mosaics of region A and B which are free of artefacts. These high-resolution radio images(with beamFWHM of 6 “)of the ATLBS survey regions cover 8.42 square degrees sky area with rms noise 72 µJy beam−1 and are of exceptional quality in that there are no imaging errors or artifacts above the thermal noise over the entire field of view. The images have excellent surface brightness sensitivity and hence provide good representation of extended emission components associated with radio sources. Optical Imaging of ATLBS Survey The ATLBS survey region has been also observed in SDSS r band, specifically for providing information about the galaxies hosting radio sources observed in ATLBS survey as well as galaxies in the neighbourhood of the radio sources. The optical observations were carried out using the CTIO 4 meter Blanco Telescope in Chile and using theMOSAICIIimager,whichisamosaicof8CCDs. In total, 28 optical images were created from the optical data. Each image was formed from a set of 5 dithers, using which spurious sources in the images were rejected. The final images are complete down to a magnitude of 22.75. Radio Source Counts Using the sensitive radio and optical images, a study of radio source counts was carried out. This study made use of some novel strategies and algorithms to generate a source list and correct it for various biases to obtain the radio source counts. More specifically, care was taken to identify sources with low surface brightness by making use of low resolution images for initial identification, and using multiple indicators (including optical images) to identify components of sources. The blending issues inherent in using low resolution images has been avoided using higher resolution images to identify blended sources. Thus, use of low resolution images( beam FWHM =50”′) almost completely removes effects of resolution bias and the use of high resolution images avoids blending issues. These strategies, together with use of optical images to locate candidate galaxy hosts and a careful visual examination of resolved and complex sources instead of automated classification ensures that the ATLBS catalog is a ‘source catalog’ as opposed to a ‘component catalog’. The distinction between ‘sources’ (which are single sources) as opposed to components(parts of a single source appearing separate) is crucial in estimating the true source counts. The source list was used toestimatetheradiosourcecountsdownto0.4 mJy. Comparing the counts with previous work shows that the ATLBS counts are systematically lower and the upturn in sub-mJy source counts has not been found down to the noise limited flux densities probed. The systematically low counts for ATLBS relative to most previous studies are attributed to the ATLBS counts representing sources as opposed to components, as well as corrections for noise bias as well as clustering effects that may affect source counts derived from the small sky coverage typical of deep surveys. This study also demonstrates the substantial difference in counts that result from using component catalogs as opposed to source catalogs: at 1 mJy flux density component counts may be as much as 50% above true source counts. This implies that automated image analysis for counts may be dependent on the ability of the imaging to reproduce connecting emission with low surface brightness as well as the ability of the algorithm to recognize sources, which require that source finding algorithms effectively work with multi-resolution and multi-wavelength data. Galaxy Environments of Extended Radio Sources in ATLBS Survey A study of the galaxy environments of the extended sources in the ATLBS survey was carried out using the optical images. This study of the environments of radio sources from the ATLBS survey is restricted to those that are extended and hence to a subset of the ATLBS-ESS(Extended Source Sample) sources. Briefly, the ATLBS-ESS subsample consists of 119 radio sources that have angular size ex-ceeding0’.5. Applying a red shift cut(to exclude sources with high red shifts whose optical environment may be beyond the depth of the optical images) as well as other constraints(such as availability of optical magnitudes of the host galaxy), a sub-sample of 43 sources was formed, including sources of diverse radio morphologies(FRI/FRII, WATs and HTs)as well as7 radio sources which are highly asymmetric in their radio morphology. For these sources, where no spectroscopic data was available, a red shift estimate was obtained from a magnitude-red shift relation derived from other sources in the ATLBS survey. Using the optical images convolved with a matched filter(following the prescription from Postman et al. (1996))consisting of a radial and magnitude filter, smoothed maps were formed for each source in the sample. These give the likelihood of a cluster being present in a given position in the map (in this case the location of interest being the position of the radio source in the map). Further, five parameters were defined in this study, which give estimates of the angular anisotropy of galaxy density around the axis of the radio source. This method used to quantify environmental asymmetry for the study presented in the thesis is new. The parameters defined thus were used to examine the environments of radio sources in the sample over a wide range in red shift. Specifically a comparison of FRI/FRII environments was made in two different red shift regimes(above and below z = 0.5) and it was found that the FRI and FRII sources inhabit environments of similar richness at low and high red shifts, with no evidence for red shift evolution. The WAT and HT sources were(as expected from earlier studies in literature)found in the most dense environments. Examination of the anisotropy parameters for the asymmetric radio sources clearly showed the influence environment has on radio source morphology, specifically in that the higher density of galaxies was found on the shorter side of the radio sources in almost all cases. Images and Other Resources The radio and optical images are an excellent resource for examining with auto-mated algorithms for source finding, parameter fitting, and morphological classification, and as a resource for testing such algorithms that would be used on upcoming all-sky continuum surveys with the LOFAR and ASKAP/SKA. The techniques and methods developed and presented in the thesis may be used in future studies of radio source populations.