Some problems which arise in the analysis and design of multilayer filters are discussed in this thesis. The filters consist of sequences of parallel-sided media which reflect and transmit electromagnetic radiation. The cases considered are those appropriate to the optical region of the spectrum although the analysis is quite general. In the optical region, the refractive index of a thin film is generally measured by the Abeles method, which entails determining the angle of incidence at which the film and the bare substrate have the same value of Rp. The presence of a small amount of absorption can produce errors in measurements of this kind. Two ways of estimating the magnitude of this error are given. Considerable broadening of the reflectance band of a multilayer may be obtained by 'staggering' the layer thicknesses in such a way that they form either an arithmetic or geometric progression. Results are shown for fifteen, twenty-five and thirty-five layers. The presence of the narrow band transmission peaks exhibited by the symmetric filters is explained, and the advantages of the use of this type of filter as an interference filter arediscussed. A closed form expression for the matrix product of staggered layers is obtained for the case when the difference in thickness is small. A 'least squares' method of filter design is introduced. This method may be used either to design a filter automatically if no initial design is available, or to 'refine' an existing design. The method is applied to the design of antireflection coatings, beam splitters, low-and high-pass filters and broad-band high reflectance coatings. In addition, one or two well-known filter designs are used to test the method.