This series of short lectures presents in a dense, elegant and clear way the fundamental notions and facts of classical stochastic calculus, with some enlightning examples. The choice of not including the proofs allows, as a counterpart, to develop the theory in few pages, and to stress more on intuitive ideas than on technics. Thus, in six beautiful lectures, are introduced and discussed successively: Brownian motions; martingales; semimartingales; stochastic integration; Itô's formula; stochastic differential equations; Markov processes; diffusions and flows; iterated stochastic integrals; chaotic representation; structure equations for normal martingales.
