Reflection high-energy electron diffraction (RHEED) is an experimentally simple technique, and yet a powerful one for examining the structure of a substrate surface and for monitoring the surface crystal structure and the crystallographic orientation of thin films during their growth. However, it can be difficult to learn to interpret the RHEED patterns of new materials, because a practical and adequately detailed introduction to the technique is not generally available. To address this need, we develop the geometrical principles of RHEED; using the kinematic approximation, we show how a particular point of the sample surface’s reciprocal net gives rise to a diffraction maximum at a particular location on the RHEED viewing screen. We explain the origins of “reciprocal lattice rods,” RHEED streaks, and Laue rings. We show how to calculate the streak spacing, and clarify the basic effect on the RHEED pattern of using a nonzero angle of incidence for the incident beam. Crystalline nets, reciprocal nets, and their RHEED patterns are derived for both (001) and (111) silicon surfaces and are compared to experimentally obtained patterns. © 1990, American Vacuum Society. All rights reserved.