This book contains almost 500 problems and solutions in the fields of special relativity, general relativity, gravitation, relativistic astrophysics and cosmology. The collection is motivated by a simple premise: that the most important content of this field does not lie in its rigorous axiomatic development, nor, necessarily, in its intrinsic aesthetic beauty, but rather does lie in computable results, predictions, and models for phenomena in the real universe. Accordingly, we have aimed for problems whose statement is broadly understandable in physical terms and have tried to "make their statement independent of notational conventions. We hope to awaken the reader's curiosity. ("Now how would one show that...?") We have steered clear of purely technical problems, found in texts, of the form "prove equation 17.4.38." In our solutions we also try to show the reader "good" ways to compute things, methods and tricks which can vastly reduce the labor of a plug-in and grind-away approach, but we also try to avoid the opposite pitfall of introducing too much confusing but powerful "formalism for an easy problem. There is often a lot of leeway in this balance, and the reader should not be surprised if his solutions use a rather smaller (or larger) set of calculational tools.