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The theory of intermolecular forces has advanced very greatly in the last few decades. Simple empirical models are no longer adequate to account for the detailed and accurate experimental measurements that are now available, or to predict properties such as the structures of molecular crystals reliably. At the same time computational methods for calculating intermolecular forces have improved enormously, so that it is possible to construct much more accurate intermolecular potential energy functions for much larger systems than was possible twenty years ago. The Theory of Intermolecular Forces describes these advances. It sets out the mathematical techniques that are needed to describe molecular properties and the ways that they contribute to the interactions between molecules. There is a detailed account of the use of multipole moments to describe electrostatic and related interactions, and both Cartesian and spherical tensor methods are described. Perturbation theories of intermolecular interactions, in particular the widely-used SAPT and SAPT-DFT methods, are discussed in detail. The many analytic models of intermolecular potentials are described and discussed, and the methods used to predict experimental properties from them are described.