An important class of optical systems are those that use mirrors. For a mirror, the ray angle of incidence equals the ray angle of reflection, and there is no light dispersion. Using mirrors for imaging has the advantages of allowing for large element diameters, no intrinsic chromatic aberrations, lesser surface curvature for a given optical power, and potential compactness as the beam of light can be folded. The disadvantages are a central obscuration, more sensitivity to surface errors, the need to include baffles to control stray light, and sometimes fewer degrees of freedom to control aberration. Mirror systems, however, use aspheric surfaces to help control aberration. Lenses can be used in conjunction with mirrors to enhance performance. Optical systems that use both mirrors and lenses are known as catadioptric. This chapter discusses some basic mirror systems. The discussion uses aberration coefficients to determine primary aberrations and to find solutions that can later be optimized with real ray tracing.