Hertweck, T., 2020. Rays in constant-gradient velocity fields: a tutorial. Journal of Seismic Exploration, 29: 527-548. Ray theory is a high-frequency approximation to the wave equation and can be used to calculate seismic wavefields in 3D inhomogeneous Earth models. In general, the corresponding raytracing equations have to be solved numerically. However, for certain simplified models such as, for instance, an Earth described by a constant-gradient velocity field, the solutions of the raytracing system can be obtained analytically. In this tutorial the fundamental concepts are explained, the most important equations and their solution are presented, and examples highlighting the analytical nature of describing rays in constant-gradient velocity fields are shown. This tutorial is meant to complement text books where for space reasons detailed mathematical derivations are often neglected.