The Sub-millimetre and Millimetre Radiometer (SMR) is the main instrument on the Swedish, Canadian, Finnish and French spacecraft Odin. It consists of a 1.1 metre diameter telescope with four tuneable heterodyne receivers covering the ranges 486-504 GHz and 541-581 GHz, and one fixed at 118.75 GHz together with backends that provide spectral resolution from 150 kHz to 1 MHz. This Letter describes the Odin radiometer, its operation and performance with the data processing and calibration described in Paper II