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The Transient Double-beam Spectrograph (TDS) is designed for optical low-resolution observations of non-stationary and extragalactic sources with the 2.5-m telescope of Caucasus Mountain Observatory of the Sternberg Astronomical Institute. It operates simultaneously in a short-wavelength (360--577 nm, reciprocal dispersion 1.21 A/pixel, resolving power R=1300 with a 1 arcsec slit) and long-wavelength (567--746 nm, 0.87 A/pixel, R=2500) channels. The light is split by a dichroic mirror with a 50% transmission at 574 nm. In the "blue" channel, the automatic replacement of the grating by a grism with a double resolving power is possible. Two CCD-cameras use E2V 42-10 detectors cooled down to $-70^\circ$C with a readout noise of 3 $e-$ at a readout rate of 50 kHz. The spectrograph is equipped with a back slit viewer camera and a calibration unit allowing to record a comparison spectrum from a hollow cathode lamp for wavelength calibration or from an LED source with a continuous spectrum (the "flat field") to take into account the vignetting and uneven slit illumination. The throughput of the entire optical path without slit loss is 20% at the zenith in the "blue" and 35% in the "red" channel. Excluding the atmosphere and the telescope, the efficiency of the TDS itself reaches a maximum of 47% and 65% respectively. The spectrograph is permanently mounted in the Cassegrain focus of the 2.5-m telescope of CMO SAI MSU sharing the port with a wide-field photometric CCD-camera. The spectrograph is fed by the light from a folding mirror introduced into the optical path. Since November 2019, TDS has been used for regular observations of non-stationary stars and extragalactic sources up to 20-th mag in a 2-h exposure with a signal-to-noise ratio >5 per pixel.