Some aspects of the representation theory of Lie groups are the subject of this monograph. However, it is not written in the conventional tensor notation but instead in terms of an equivalent diagrammatic notation. We shall refer to this style of carrying out group-theoretic calculations as*birdtracks*(and so do reputable journals [51]). The advantage of diagrammatic notation will become self-evident, I hope. Two of the principal benefits are that it eliminates “dummy indices,” and that it does not force group-theoretic expressions into the 1-dimensional tensor format (both being means whereby identical tensor expressions can be made to look totally