The HERMES experiment is collecting data on inclusive and semi-inclusive deep inelastic scattering of polarised positrons from polarised targets of Il, D, and He-3. These data give information on the spin structure of the nucleon. This paper describes the forward angle spectrometer built for this purpose. The spectrometer includes numerous tracking chambers (micro-strip gas chambers, drift and proportional chambers) in front of and behind a 1.3 T.m magnetic field, as well as an extensive set of detectors for particle identification (a lead-glass calorimeter, a pre-shower detector, a transition radiation detector, and a threshold Cherenkov detector). Two of the main features of the spectrometer are its good acceptance and identification of both positrons and hadrons, in particular pions. These characteristics, together with the purity of the targets, are allowing HERMES to make unique contributions to the understanding of how the spins of the quarks contribute to the spin of the nucleon. (C) 1998 Elsevier Science B.V. All rights reserved.