Quantum Probability for Probabilists

These notes contain all the material accumulated over six years in Strasbourg to teach'Quantum Probability'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'Lecture Notes'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'for probabilists'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'Quantum Probability', the main topic is'Quantum Stochastic Calculus', a field which has recently got official recognition as 81825 in the Math.