  We review the current theory of how galaxies form within the cosmological
framework provided by the cold dark matter paradigm for structure formation.
Beginning with the pre-galactic evolution of baryonic material we describe the
analytical and numerical understanding of how baryons condense into galaxies,
what determines the structure of those galaxies and how internal and external
processes (including star formation, merging, active galactic nuclei etc.)
determine their gross properties and evolution. Throughout, we highlight
successes and failings of current galaxy formation theory. We include a review
of computational implementations of galaxy formation theory and assess their
ability to provide reliable modelling of this complex phenomenon. We finish
with a discussion of several "hot topics" in contemporary galaxy formation
theory and assess future directions for this field.
