Optical designs are presented for the Maunakea Spectroscopic Explorer (MSE) telescope. The adopted baseline design is a prime focus telescope with a segmented primary of 11.25m aperture, with speed f/1.93 and 1.52° field-of-view, optimized for wavelengths 360-1800nm. The Wide-Field Corrector (WFC) has five aspheric lenses, mostly of fused silica, with largest element 1.33m diameter and total glass mass 788kg. The Atmospheric Dispersion Corrector (ADC) is of the compensating lateral type, combining a motion of the entire WFC via the hexapod, with a restoring motion for a single lens. There is a modest amount of vignetting (average 5% over the hexagonal field); this greatly improves image quality, and allows the design to be effectively pupil-centric. The polychromatic image quality is d80<0.225"/0.445" at ZD 0/60° over more than 95% of the hexagonal field-of-view. The ADC action allows adjustment of the plate-scale with zenith distance, which is used to halve the image motions caused by differential refraction. A simple design is presented for achieving the required ADC lens shifts and tilts. A two-mirror design was also undertaken for MSE, but was not selected. This is a 12.3m F/2.69 forward Cassegrain design, with a 2.75m diameter M2, and three silica lenses, of largest diameter 1.33m. The field-of-view is again 1.52°. The f/0.95 primary makes the design remarkably compact, being under 10m long. The ADC action involves a small motion of M2 (again via a hexapod), and shifts and tilts of a single lens. The design is effectively pupil-centric, with modest vignetting (5.9% average). The image quality is virtually identical to the prime focus design.