The standard cosmological model is an impressive theory that explains well the observed evolution and structure of the Universe, but we know the theory has to be incomplete since it does not explain the initial conditions of the Big Bang. Inflation is an extension to the model that hypothesizes an incredibly brief period of accelerating expansion in the first moments after the Big Bang to explain how the required initial conditions were met. Most theories of Inflation predict a stochastic background of gravitational waves would have been produced, which would have imprinted a characteristic curl-like B-mode pattern into the polarization of the cosmic microwave background (CMB), and finding these B-modes would provide direct evidence for Inflation, opening a new window into the high-energy physics of the early Universe. The BICEP/Keck Array telescopes are a series of small aperture, polarization-sensitive microwave telescopes expressly optimized for observing the degree-angular scale CMB where the B-mode signal is predicted to peak. Continuous mapping since 2010 of ~1% of the low-foreground sky from the South Pole has produced maps in multiple frequencies bands which result in the tightest constraint on Inflationary gravitational waves to date: r < 0.072 using data through the end of 2015. In this dissertation we review the end-to-end analysis of the BICEP/Keck Array data, from timestreams to cosmological parameter estimation. Along the way, we will detail two specific contributions the author has made for the upcoming analysis results. The first concerns a correction made to the low-level timestream processing, discovered while analyzing the data from the newest telescope for the first time. The second topic is the introduction of new algorithms and parameter choices for the E/B purification process that improves the purification quality. Finally, we conclude by previewing the anticipated result of including three additional years of previously unreported data which has the potential to improve current cosmological parameter constraints on r by a factor of two.