The book "Computational Methods for Astrophysical Fluid Flow" offers a comprehensive introduction to modern numerical techniques for analyzing compressible flows, particularly in the context of astrophysical applications. It places special emphasis on high-resolution methods for shock capturing, which are based on Riemann solvers. The authors explain the application of these methods, including the PPM technique, and demonstrate their use in large-scale simulations of supernova explosions and astrophysical jets. The second and third sections of the book focus on radiation hydrodynamics and showcase the advantages of adaptive grids through various stellar simulations that exhibit clear shock front structures. Through four lectures, the reader is guided from basic numerical methods for solving hyperbolic partial differential equations to complex simulation codes for specific astrophysical problems. The book highlights the powerful capabilities and challenges of computational astrophysics and addresses complex topics such as gravity, magnetic fields, reactive flows, and relativity.