Abstract
Tensor and spinor methods are used to derive branching rule formulae for the embedding of one classical Lie group in another. These formulae involve operations on S-functions. By the judicious use of identities satisfied by certain infinite series of S-functions, they are reduced to forms which may be used very efficiently. Eleven sets of the branching rule formulae derived are as simple as possible, in that they involve only a sum of positive terms, whilst four other sets involve some negative terms which ultimately cancel. The advantage of using a composite notation, both for mixed tensor and for spinor representations, is made apparent. A comparison is made with methods used to derive branching rules based on mapping from one weight space to another.