Quantum Probability was initiated by von Neumann as a new, intrin￾sically probabilistic Hilbert space theory of operator observables. Starting
with the 80’s of the last century the field was greatly enlarged and devel￾oped into a non-commutative analogue of Kolmogorov’s theory of stochas￾tic processes. One of its aims is to clarify the probabilistic foundations of
quantum theory and its statistical interpretation. The basic problems cen￾tre around non-commutative independence (including freeness), quantum
dynamic dependence (entanglement) and quantum stochastic dependence
(non-commutative Markov processes). Quantum Probability is now a het￾erogeneous subject with many connections to other areas of mathematics
and physics. On the pure mathematics side, it interacts with infinite dimen￾sional functional and non-commutative harmonic analysis, operator algebra
and operator space theory, non-commutative dynamics, non-commutative
K-theory.