Quantum Probability for Probabilists

These notes contain all the material accumulated over six years in Strasbourg to teach "e;Quantum Probability"e; to myself and to an audience of commutative probabilists. The text, a first version of which appeared in successive volumes of the Seminaire de Probabilite8, has been augmented and carefully rewritten, and translated into international English. Still, it remains true "e;Lecture Notes"e; material, and I have resisted suggestions to publish it as a monograph. Being a non-specialist, it is important for me to keep the moderate right to error one has in lectures. The origin of the text also explains the addition "e;for probabilists"e; in the title : though much of the material is accessible to the general public, I did not care to redefine Brownian motion or the Ito integral. More precisely than "e;Quantum Probability"e; , the main topic is "e;Quantum Stochastic Calculus"e; , a field which has recently got official recognition as 81825 in the Math.