Graduate students and researchers in astrophysics and cosmology need a solid understanding of a wide range of physical processes. This clear and authoritative textbook has been designed to help them to develop the necessary toolkit of theory. Assuming only an undergraduate background in physics and no detailed knowledge of astronomy, this book guides the reader step by step through a comprehensive collection of fundamental theoretical topics. The book is modular in design, allowing the reader to pick and chose a selection of chapters, if necessary. It can be used alone, or in conjunction with the forthcoming 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 all the key concepts such as radiative processes, spectra, fluid mechanics, plasma physics and MHD, dynamics of gravitating systems, general relativity, and nuclear physics. Each topic is developed methodically from undergraduate basic physics. Throughout, the reader's understanding is developed and tested with carefully structured 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 cutting-edge research in astrophysics and cosmology.