Probability is concerned with the mathematical analysis of random phenomena. It is younger than most other areas of Mathematics, as it originated with the study of games of chance by Pascal and Fermat (1654), since then it has become indispensable for dealing with randomness in almost all branches of science. Today, in addition to its strong position as a full-fledged area within mathematics - and its interactions with analysis, partial differential equations, geometry, combinatorics, number theory and mathematical physics - probability forms the language of statistics and of the quantitative social sciences. It is essential in the discovery and study of macroscopic regularities that occur when large systems of particles, organisms, or agents, interact according to the laws of physics, biology, or economics, in the study of population genetics and of the genome, in the study of how signals are transmitted through a noisy channel, and then recovered, in the design and analysis of large-scale communication, neural or queueing networks, and of algorithms for combinatorial optimization, computerized tomography, signal processing, pattern recognition, and so on. A central role in several of these applications is played by the development of stochastic analysis over the last 70 years, starting with the pioneering work of K. Ito in 1942.