  We discuss a version of \'Ecalle's definition of resurgence, based on the
notion of endless continuability in the Borel plane. We relate this with the
notion of \Omega-continuability, where \Omega\ is a discrete filtered set, and
show how to construct a universal Riemann surface X_\Omega\ whose holomorphic
functions are in one-to-one correspondence with \Omega-continuable functions.
We then discuss the \Omega-continuability of convolution products and give
estimates for iterated convolutions of the form \hat\phi_1*\cdots *\hat\phi_n.
This allows us to handle nonlinear operations with resurgent series, e.g.
substitution into a convergent power series.
