Places the A-P-S index theorem in an analytic framework analogous to that provided by the theory of pseudodifferential operators for the A-S theorem. The A-P-S theorem is used to discuss some important aspects of geometry and analysis on manifolds with boundary. The author begins by stating and proving the theorem, then uses the remaining chapters to flesh out these initial concepts. An introduction to the "b" category and the related calculus of b-pseudodifferential operators on boundaried compact manifolds is given. Annotation copyright Book News, Inc. Portland, Or.