This monograph discusses the existence and regularity properties of local times associated to a
continuous semimartingale as well as excursion theory for Brownian paths. Realizations of
Brownian excursion processes may be translated in terms of the realizations of a Wiener process
under certain conditions. With this aim in mind the monograph presents applications to topics
which are not usually treated with the same tools e.g.: arc sine law laws of functionals of
Brownian motion and the Feynman-Kac formula.
