Modern cosmology and high energy astrophysics have become interdisciplinary research subjects and new graduate students are now expected to assimilate a broad range of physical concepts. This innovative book provides a clear and pedagogical introduction to research in these areas through a series of problems and answers. The problems are designed to develop each core topic in a simple and coherent way and full solutions are provided to make this book completely self-contained. The first half of the book covers the core subjects of astrophysical processes, gravitational dynamics, radiative processes, fluid mechanics and general relativity. The second half uses these concepts to develop modern cosmology: topics include the Friedmann model and thermal history, dynamics of dark matter and baryons in an expanding universe, physics of high-redshift objects and the very early universe. This unique self-study textbook will be of key interest to graduate students and researchers in cosmology, astrophysics, relativity and theoretical physics. It is particularly well suited to graduate-level courses.