The cores of galaxy clusters contain the most massive galaxies in the Universe, the brightest cluster galaxies. These galaxies are unique compared to their counterpart galaxies outside of clusters as they have much brighter cores, and vast spatially- extended stellar envelopes. The theoretical picture of how they reached their huge masses relied on the idea of gradual stellar mass growth during the second half of the history of the Universe. However, recent observational evidence of highly-overdense protoclusters, the progenitors of these galaxies, demonstrates that some brightest cluster galaxies may have assembled within the first few billion years after the Big Bang – seemingly contradicting our theoretical predictions. I include my theoretical work that shows the short timescales over which these observed protoclusters trans- form into the brightest cluster galaxies and discuss the likelihood of finding these rare protoclusters in the early Universe. To push our understanding of the rapid evolution of these galaxies even further for- ward demands the use of numerical simulations due to the highly coupled, non-linear astrophysical processes that occur during the process. In this dissertation, I include improvements to our numerical models of hydrodynamical turbulence and supermas- sive black holes that I incorporated into a state-of-the-art hydrodynamical+gravity simulation code, in effort to provide the groundwork to improving our understanding of the build-up of the brightest cluster galaxies in the early Universe, and galaxy evolution in general. / Graduate

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