This innovative book provides a clear and pedagogical introduction to research through a series of problems and answers. The author has designed the problems to develop each core topic in a simple and coherent way, and he provides full solutions 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, the dynamics of dark matter and baryons in an expanding universe, the 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.