Quantum stochastics The classical probability theory initiated by Kolmogorov and its quantum counterpart pioneered by von Neumann were created at about the same time in the 1930s but development of the quantum theory has trailed far behind. Although highly appealing the quantum theory has a steep learning curve requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic self contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces bounded linear operators and classical Markov processes. From there the book introduces additional tools from analysis and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise quantum stochastic calculus stochastic quantum differential equations quantum Markov semigroups and processes and large time asymptotic behavior of quantum Markov semigroups It is widely known that the classical probability theory initiated by Kolmogorov and its quantum counterpart pioneered by von Neumann were both created at about the same time in1930s. However the subsequent developments of the latter have trailed far behind the former ones. This is perhaps because development of a theory of quantum stochastics requires an unusually large number of tools from operator theory and perhaps also because the probabilistic and analytical tools for understanding sample path behaviors of quantum stochastic processes have yet to be developed