The motions of test particles and light, described within General Relativity by the geodesic equation, are an effective possibility to explore the physics of gravitational fields. Although a majority of gravitational effects can be discussed using approximations and numerics, the appealing goal of a systematic study of all effects can only be achieved using analytical methods. This book is devoted to an extensive study of geodesics in a wide variety of space-times using analytical methods including not only a complete classification of orbit types but also analytic solutions of the geodesic equations. Starting with the static and spherically symmetric Schwarzschild space-time, the geometries become more and more complex, in particular including a cosmological constant. The powerful methods presented here can be used for geodesics in every type D space-time and are applicable to even more general settings.