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Vingt cinq articles ont ete selectionnes pour leur interet historique et scientifique des 14 premiers volumes du Seminaire de Probabilites, tous epuises.

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Addressed to both pure and applied probabilitists, including graduate students, this text is a pedagogically-oriented introduction to the Schwartz-Meyer second-order geometry and its use in stochastic calculus. P.A. Meyer has contributed an appendix: "A short presentation of stochastic calculus" presenting the basis of stochastic calculus and thus making the book better accessible to non-probabilitists also. No prior knowledge of differential geometry is assumed of the reader: this is covered within the text to the extent. The general theory is presented only towards the end of the book,...

The 31 papers collected here present original research results obtained in 1995-96, on Brownian motion and, more generally, diffusion processes, martingales, Wiener spaces, polymer measures.

Kunita, H.: Stochastic differential equations and stochastic flows of diffeomorphisms.-Elworthy, D.: Geometric aspects of diffusions on manifolds.-Ancona, A.: Theorie du potential sur les graphs et les varieties.-Emery, M.: Continuous martingales in differentiable manifolds. ​

The tradition of specialized courses in the Seminaires de Probabilites is continued with A. Lejay's Another introduction to rough paths. Other topics from this 42nd volume range from the interface between analysis and probability to special processes, Levy processes and Levy systems, branching, penalization, representation of Gaussian processes, filtrations and quantum probability.