The spectrometer on INTEGRAL (SPI) is one of the two main telescopes of the future INTEGRAL observatory. SPI is made of a compact hexagonal matrix of 19 high-purity germanium detectors shielded by a massive anticoincidence system. A HURA type coded aperture modulates the astrophysical signal. The spectrometer system, its physical characteristics and performances are presented. The instrument properties such as imaging capability, energy resolution and sensitivity have been evaluated by means of extensive Monte-Carlo simulations. With the expected performances of SPI, it will be possible to explore the gamma-ray sky in greater depth and detail than it was possible with previous gamma-ray telescopes like SIGMA, OSSE and COMPTEL. In particular, the high-energy resolution will allow for the first time the measurement of gamma-ray line profiles. Such lines are emitted by the debris of nucleosynthesis and annihilation processes in our Galaxy. Lines from these processes have already been measured, but due to the relatively poor energy resolution, details of the emission processes in the source regions could not be studied. With the high-resolution spectroscopy of SPI such detailed investigations will be possible.