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This book is not in any sense complete or exhaustive, and it is not meant to be. Its subject, theoretical astrophysics, is vast and cannot possibly be comprehensively covered in a single volume. This book has a rather different purpose. It is intended as a textbook for students who have a reasonably complete knowledge of the material usually taught in the introductory courses on theoretical physics: classical mechanics, electrodynamics, quantum mechanics, and thermodynamics. Building upon this assumed foundation, this book adds material typically not covered by the introductory lectures, but required for research work in theoretical astrophysics. It may also be useful as a resource for researchers. Arguably the most important extensions are radiation processes, hydrodynamics, plasma physics and magnetohydrodynamics, and stellar dynamics. This book provides introductions to these four areas. It is structured into four main chapters and an initial chapter summarising some essential theoretical concepts which the following chapters build upon