This lecture series mixes two fundamental techniques for the study of Brownian motion, namely stochastic calculus and excursion theory. The local time can be used to analyze stochastic differential equations while realizations of Brownian excursion processes may be translated in terms of the realization of a Wiener process under certain conditions. Both from an educational (theoretical development) point of view and a research (application development) point of view, it is important and relevant to learn these two techniques related to Brownian motion.