This paper describes the Heterodyne Instrument for the Far-Infrared (HIFI), to be launched onboard of ESA's Herschel Space Observatory, by 2008. It includes the first results from the instrument level tests. The instrument is designed to be electronically tuneable over a wide and continuous frequency range in the Far Infrared, with velocity resolutions better than 0.1 km/s with a high sensitivity. This will enable detailed investigations of a wide variety of astronomical sources, ranging from solar system objects, star formation regions to nuclei of galaxies. The instrument comprises 5 frequency bands covering 480-1150 GHz with SIS mixers and a sixth dual frequency band, for the 1410-1910 GHz range, with Hot Electron Bolometer Mixers (HEB). The Local Oscillator (LO) subsystem consists of a dedicated Ka-band synthesizer followed by 7 times 2 chains of frequency multipliers, 2 chains for each frequency band. A pair of Auto-Correlators and a pair of Acousto-Optic spectrometers process the two IF signals from the dual-polarization front-ends to provide instantaneous frequency coverage of 4 GHz, with a set of resolutions (140 kHz to 1 MHz), better than