At the turn of the century, astronomers started to chart our Galaxy, the Milky Way, by studying the distribution, kinematics, and chemical abundances of different types of stars. Our understanding of the Milky Way has its foundation in their pioneering work. Today, astronomers are faced with an equally daunting task: mapping the observable Universe. Their probes are not stars but galaxies. While it is true that 4-m class telescopes have been in existence for decades, the task of cataloging countless galaxies sprinkled like grains of sand across the Universe seemed nearly impossible to astronomers armed with photographic plates. Their dismay was easily understandable considering the fact that an entire night was required to collect enough light to determine the redshift of a single, relatively nearby galaxy.
Nowadays, astronomers can measure hundreds of redshifts in one night using the same telescopes. This tremendous gain in telescope efficiency comes from recent advances in sensitive digital detectors (known as charge-coupled devices or CCDs) and the advent of multi-object spectrographs. Equipped with these powerful ``redshift machines'', astronomers set out to count galaxies and measure their spatial distribution. They had hoped to determine the values of fundamental cosmological constants linked to the topology of the Universe. It turned out otherwise. There were simply too many distant galaxies compared to what had been expected from studies of the neighborhood of the Milky Way. This puzzling observation became known as the faint galaxy excess problem. Though it has been the topic of extensive study in the astronomical literature, it has proven to be a particularly difficult problem to solve. Models proposed by astronomers to explain the distant Universe often had profound (and unforeseen) consequences on local galaxy properties 
for example, the thickness of spiral disks, and the metallicity of dwarf galaxies, to name two.
Thanks to adaptive optics systems which can correct aberrations in astronomical images introduced by the Earth's atmosphere, it is now possible to study distant galaxies in greater detail and measure their masses directly from their internal velocity fields. Internal kinematics is a novel technique to tackle the faint galaxy excess problem a technique that goes beyond redshift surveys. These surveys can provide information only on the global evolution of a galaxy population, whereas internal kinematics can be used to trace evolution in individual galaxies. The goal of this thesis is to use internal kinematics to probe the nature of distant galaxies and understand the manner in which they evolve into the local galaxy population. As the reader will see, the task is extremely challenging since it involves working at the limits of detection and spatial resolution of current telescopes.
This thesis is organized into nine chapters. Chapter 
starts by showing how galaxy differential number counts N(m) and galaxy redshift distributions N(z) led to the faint galaxy excess problem. Chapter describes faint galaxy models based on luminosity evolution and mergers. These two chapters are intended to give the reader the background information needed to understand the motivation behind this thesis.
Chapter explains how the internal kinematics of distant galaxies can be used to test faint galaxy models. Previous studies are discussed, and the goals of our survey, which was conducted at the Canada-France-Hawaii Telescope (CFHT), are given. Sample selection, observations and data pre-processing are explained in Chapter . Chapter shows how synthetic rotation curves, a pattern-recognition method based on a parametric fitting model, can be used to optimally extract information on the internal kinematics of faint galaxies from very low signal-to-noise data. Topics covered in this chapter include the fitting model, the Metropolis algorithm used for finding parameter values, and the implementation of the synthetic rotation curve method within the IRAF environment.
Chapter presents the results of the CFHT internal kinematics survey. Internal kinematics is compared to broad-band galaxy morphologies and surface brightness profiles, [OII] morphologies and rotation velocities expected on the basis of the local Tully-Fisher relation.
The results are discussed in Chapter . Kinematical evidence for luminosity evolution is presented. The effects of uncertainties in the local Tully-Fisher on this kinematical evidence are explained. A comparison with other works leads to the exciting conclusion that luminosity-dependent luminosity evolution is the cause of the faint galaxy excess problem.