Computational astrophysics is a new and quickly-growing discipline. This book outlines the fundamentals for computational astrophysics, focusing on the use of the Astronomical Multipurpose Software Environment (AMUSE), which is a general-purpose simulation environment in astrophysics written in Python. AMUSE allows you to combine existing solvers to build new applications that can be combined again to study gradually more complex situations. This enables the growth of multi-physics and multi-scale application software in a hierarchical fashion, testing each intermediate step, as the complexity of the software continues to increase. All examples in the book are associated with codes that run on a simple laptop or workstation. All figures are reproducible with a simple script and all scripts are available online to be downloaded and run accordingly.