| Summary: | The evolution of galaxies in the cluster environment is a complex process, with many outstanding questions. A wide range of galaxy morphologies, colours, sizes and luminosities are found in clusters, the least studied of which are the faint galaxy populations. Studying the faint end of the galaxy luminosity distribution may provide a valuable insight into the evolution of galaxies in cluster environments. The largest of these faint galaxies are classified as Ultra-Diffuse galaxies (UDGs). UDGs are low surface brightness galaxies with a very low stellar mass component, however they have sizes comparable to the Milky Way. These galaxies are hard to detect and classify as they are very faint. To survive in the cluster environments, where they have been observed, these galaxies must contain significant amounts of dark matter as the strong tidal fields would normally tear diffuse low-mass galaxies apart. The high abundance of UDGs in clusters has only recently been recognized, therefore identifying and measuring their properties is key to understanding how they are formed and continue to exist. In this thesis, I search for low surface brightness galaxies, spanning from typical dwarf galaxies to UDGs, in 16 low redshift (z< b/a >= 0.52. The number of faint galaxies in clusters follows a power-law with respect to the cluster halo mass, N ∝ M1.05±0.45, determined through bootstrap resampling. This shows that the number of UDG candidates increases as the cluster halo mass increases.
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