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This book tries to present some of the main aspects of the theory of Probability in Banach spaces, from the foundations of the topic to the latest developments and current research questions. The past twenty years saw intense activity in the study of classical Probability Theory on infinite dimensional spaces, vector valued random variables, boundedness and continuity of random processes, with a fruitful interaction with classical Banach spaces and their geometry. A large community of mathematicians, from classical probabilists to pure analysts and functional analysts, participated to this common achievement.The recent use of isoperimetric tools and concentration of measure phenomena, and of abstract random process techniques has led today to rather a complete picture of the field. These developments prompted the authors to undertake the writing of this exposition based on this modern point of view.This book does not pretend to cover all the aspects of the subject and of its connections with other fields. In spite of its ommissions, imperfections and errors, for which we would like to apologize, we hope that this work gives an attractive picture of the subject and will serve it appropriately.In the process of this work, we benefited from the help of several people. We are grateful to A.