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We present the design and performance of the TANSPEC, a medium-resolution $0.55-2.5~μ$m cryogenic spectrometer and imager, now in operation at the 3.6-m Devasthal Optical Telescope (DOT), Nainital, India. The TANSPEC provides three modes of operation which include, photometry with broad- and narrow-band filters, spectroscopy with short slits of 20$^{\prime \prime}$ length and different widths (from 0.5$^{\prime \prime}$ to 4.0$^{\prime \prime}$) in cross-dispersed mode at a resolving power R of $\sim$2750, and spectroscopy with long slits of 60$^{\prime \prime}$ length and different widths (from 0.5$^{\prime \prime}$ to 4.0$^{\prime \prime}$) in prism mode at a resolving power R of $\sim$100-350. TANSPEC's imager mode provides a field of view of 60$^{\prime \prime} \times 60^{\prime \prime}$ with a plate scale of 0.245$^{\prime \prime}$/pixel on the 3.6-m DOT. The TANSPEC was successfully commissioned during April-May 2019 and the subsequent characterization and astronomical observations are presented here. The TANSPEC has been made available to the worldwide astronomical community for science observations from October 2020.