The next major topic is the calculus of 6-pseudodifferential operators, since this allows the analytic properties of elliptic 6-differential operators to be examined. The treatment starts very geometrically. In particular Figure 2 of Chapter 1 will be explained. Recall from (1.24) and (1.26) that the kernels of the inverses of operators such as ь3103+ +1 can be expected to be simplest when expressed in terms of the singular coordinates (1.25). In the one-dimensional case this is rather a minor issue. In the higherdimensional examples of interest here it is more significant, as there will be a countably infinite superposition of terms like (1.26), with different constants c. To handle these systematically the properties of the coordinate change (1.25) will be examined with some care. 4.1. Inward-pointing spherical normal bundle.