On the exact simulation of (skew) Brownian diffusions with discontinuous drift This thesis is focused on the study and the exact simulation of two classes of real valued Brownian diffusions: multi skew Brownian motions with constant drift and Brownian diffusions whose drift admits a finite number of jumps. The skew Brownian motion was introduced in the sixties by Itô and McKean who constructed it from the reflected Brownian motion flipping its excursions from the origin with a given probability. Such a process behaves as the original one except at the point 0 which plays the role of a semipermeable barrier. More generally a skew diffusion with several semipermeable barriers called multi skew diffusion is a diffusion everywhere except when it reaches one of the barriers where it is partially reflected with a probability depending on that particular barrier. Clearly a multi skew diffusion can be characterized either as solution of a stochastic differential equation involving weighted local times (these terms providing the semi permeability) or by its infinitesimal generator as Markov process.