  R. B. Melrose's b-calculus provides a framework for dealing with problems of
partial differential equations that arise in singular or degenerate geometric
situations. This article is a somewhat informal short course introducing many
of the basic ideas of this world, assuming little more than a basic analysis
and manifold background. As examples, classical pseudodifferential operators on
manifolds and b-pseudodifferential (also known as totally characteristic)
operators on manifolds with boundary are discussed.
