  This survey gives a comprehensive account of quantum correlations understood
as a phenomenon stemming from the rules of quantization. Centered on quantum
probability it describes the physical concepts related to correlations (both
classical and quantum), mathematical structures, and their consequences. These
include the canonical form of classical correlation functionals, general
definitions of separable (entangled) states, definition and analysis of
quantumness of correlations, description of entanglement of formation, and PPT
states. This work is intended both for physicists interested not only in
collection of results but also in the mathematical methods justifying them, and
mathematicians looking for an application of quantum probability to concrete
new problems of quantum theory.
