This new text surveys a series of fundamental problems in astrophysics, both analytically and computationally for advanced students in physics and astrophysics. The contents are supported by over 110 class-tested Mathematical notebooks, allowing rigorous solutions to be explored in a visually engaging way. Topics covered include many classical and historically interesting problems, enabling the students to appreciate the mathematical and scientific challenges that were overcome in the subject's development. The text also shows the advantages and disadvantages of using analytical and computational methods. It will serve students, professionals, and capable amateurs to master the quantitative details of modern astrophysics and the computational aspects of their research projects.