Four lectures lead the reader from basic numerical methods for solving hyperbolic partial differential equations to the application of complex simulation codes to selected astrophysical problems. The text highlights the powerful capabilities, the use, and the pitfalls of computational astrophysics. Difficult topics pertaining to astrophysical problem solving, such as gravitation, magnetic fields, reactive flow, and relativity, are addressed. Two lectures are devoted to radiation hydrodynamics. They treat the derivation of the basic equations and numerical methods. This book will be useful to students and researchers in astrophysics and applied mathematics.