The telescope form known as the Three Mirror Anastigmat (TMA), has gained in popularity as optical manufacturing and optical test techniques have improved. TMAs are now widely used throughout the optical industry, and are described in numerous publications. These telescopes may be designed to produce output beams that are afocal (collimated) or focal. In this paper, the optimal surface shapes will be examined for both types of TMA telescopes. Optimal is defined to be the surface shapes that minimize the wavefront error (WFE). The following design constraints are applied: the entrance pupil is on the primary mirror (PM) and the system WFE is largely free of primary spherical aberration, coma, astigmatism, and field curvature. Variable design parameters include: the radius of curvature of the PM, the distance to the secondary mirror (SM) the effective focal length, and the system magnification. Additionally, many first order optical parameters are derived from this selection of inputs. In particular, the differences in wavefront error aberrations associated with focal and afocal TMAs are characterized, and it is shown that the conic constant of the PM is ideally -1, resulting in a parabolic surface shape, to achieve the lowest design residual WFE for afocal TMAs. In contrast, focal TMAs are shown to require a PM surface that is an ellipsoid, with conic constant k in the range -1 < k < 0. Example telescope designs are illustrated.