The field of galaxy formation and evolution synthesizes the physics of baryons and dark matter to describe the origin of systems such as the Milky Way and the enormous diversity of the galaxy population. The broad variation in possible formation histories and the wide range of cosmic environments make large statistical samples of galaxies essential for identifying the important physical mechanisms that govern their formation. Starting in the early 2020s, the Large Synoptic Survey Telescope (LSST) will provide an unmatched dataset for galaxy evolution studies by observing the entire southern sky in ultraviolet, optical and near-infrared wavelengths, producing multi-epoch digital images over a 10-year nominal mission that when summed will provide the deepest, wide-angle view of our Universe ever assembled. Here, we discuss the importance of LSST for deepening our understanding of galaxy formation and evolution over cosmic time. We present some outstanding problems in the field that LSST will address, and we present a roadmap of some preparatory research efforts required to make effective use of the LSST dataset for galaxy formation science.