Graduate students and researchers in astrophysics and cosmology need a solid understanding of a wide range of physical processes. This clear and authoritative book has been designed to help them to develop the necessary toolkit of theory. The book is modular in design, allowing the reader to pick and choose a selection of chapters, if necessary. It can be used alone, or in conjunction with the accompanying two volumes (covering stars and stellar systems, and galaxies and cosmology, respectively). After reviewing the basics of dynamics, electromagnetic theory, and statistical physics, the book carefully develops a solid understanding of radiative processes, spectra, fluid mechanics, plasma physics and MHD, dynamics of gravitating systems, general relativity, nuclear physics, and other key concepts. Throughout, the reader's understanding is developed and tested with problems and helpful hints. This welcome volume provides graduate students with an indispensable introduction to and reference on all the physical processes they will need to successfully tackle research in astrophysics and cosmology.