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We present the development of a compact f/7.3 (D=35 mm) three-mirror reflective telescope for the atmospheric-research microsatellite Mesospheric Airglow/Aerosol Tomography Spectroscopy (MATS). The telescope design was driven by the end users' need for a reflective wide-field (5.67°×0.91°) optic with high stray light rejection and six detection channels with separate image sensors, operating at wavelengths 270-772 nm. For the first time, a design method for wide-field off-axis telescopes-in which linear astigmatism is eliminated-was applied and tested in practice. Single-point diamond turning was used to produce two sets of 37-110 mm large free-form aluminum mirrors with surface figure errors and roughness values of 34-62 nm (RMS)/193-497 nm (PV) and 2.8-3.5 nm (RMS), respectively. A method that combines precise machining and geometry measurements (using a coordinate measuring machine) was employed to fabricate an aluminum structure to accurately position the mirrors without the need for manual alignment. The telescope was tested with a network of plate beamsplitters and filters, which define the spectral selection for the six detection channels. Imaging performance measurements were carried out using a reflective off-axis collimator, which projects imaging targets at infinite focus. A modulation transfer function (MTF) value of 0.45 at 20 lp/mm was measured at ∼760 nm (diffraction limit: 0.85) using a slanted edge target. By modeling the measured mirror surfaces in optical design software, a reoptimization of the mirror positions could be performed and an improved MTF of ∼0.75 at 20 lp/mm was predicted. The results demonstrate design- and building methods that can be utilized to make off-axis telescopes for a vast range of applications.