The conventional interpretation of quantum mechanics, though it permits a correspondence to classical physics, leaves the exact mechanism of transition unclear. Though this was only of philosophical importance throughout the twentieth century, over the past decade new technological developments, such as quantum computing, require a more thorough understanding of not just the result of quantum emergence, but also its mechanism. Quantum decoherence theory is the model that developed out of necessity to deal with the quantum-classical transition explicitly, and without external observers. In this thesis, we present a self-contained and rigrorously argued full derivation of the master equation for quantum brownian motion, one of the key results in quantum decoherence theory. We accomplish this from a foundational perspective, only assuming a few basic axioms of quantum mechanics and deriving their consequences. We then consider a physical example of the master equation and show that quantum decoherence successfully represents the transition from a quantum to classical system.