Recently, images of the inside of the human body have been produced non-invasively using nuclear magnetic resonance (nmr). The technique involves placing the patient in a strong, homogeneous magnetic field. The heart of any nmr imaging system is the magnet that produces this field and this thesis is concerned with the design and testing of such magnets. Various computer programs have been written that allow the designer to model a magnet either in terms of axisymmetric coils, or in terms of the discrete conductors that simulate the actual form of the winding. The axisymmetric program automatically optimises the design so as to produce a uniform field, and the data from this program may be used directly to generate an appropriate helical or spiral winding. These programs not only allow the designer to produce a suitable design, but also to put tolerances on the dimensions of the conductors and formers that support the winding. The problem of removing inhomogeneities produced by dimensional inaccuracies and surrounding ferromagnetic materials is also considered. A nmr probe system has been developed that allows the homogeneity of a magnet to be assessed independently of the stability of its power supply. The probe has been used for field measurements in a magnet designed using the above techniques, and the results are presented.