  The present notes are the expanded and polished version of three lectures
given in Stanford, concerning the analytic and arithmetic properties of weight
one modular forms. The author tried to write them in a style accessible to
non-analytically oriented number theoritists: in particular, some effort is
made to be precise on statements involving uniformity in the parameters. On the
other hand, another purpose was to provide an introduction, together with a set
of references, consciously kept small, to the realm of Galois representations,
for non-algebraists -- like the author. The proofs are sketched, at best, but
we tried to motivate the results, and to relate them to interesting
conjectures.
