Afocal systems are frequently used in thermal imagers to match the field of view required by the user to that required for high scan efficiency. The limitation on performance of such telescopes due to chromatic aberrations and field curvature as a function of magnification, field angle, and f/number is discussed together with some methods for reducing these aberrations. A detailed scheme is given for the analytical correction of the primary monochromatic aberrations in telescope systems. Aberrations of the pupil in such telescope systems, and their control, are discussed with respect to the radiometry of thermal imagers. Finally a number of designs of telescope systems of various magnifications are discussed in some depth, from design philosophy to performance values. The designs include refracting and reflecting systems employing both spherical and aspheric surfaces.