  We present a perturbative construction of interacting quantum field theories
on any smooth globally hyperbolic manifold. We develop a purely local version
of the Stueckelberg-Bogoliubov-Epstein-Glaser method of renormalization using
techniques from microlocal analysis. As byproducts, we describe a perturbative
construction of local algebras of observables, present a new definition of Wick
polynomials as operator-valued distributions on a natural domain, and we find a
general method for the extension of distributions which were defined on the
complement of some surfaces.
