Wick ordering of creation and annihilation operators is of fundamental importance for computing averages and correlations in quantum field theory and, by extension, in the Hudson-Parthasarathy theory of quantum stochastic processes, quantum mechanics, stochastic processes, and probability. This book develops the unified combinatorial framework behind these examples, starting with the simplest mathematically, and working up to the Fock space setting for quantum fields. Emphasizing ideas from combinatorics such as the role of lattice of partitions for multiple stochastic integrals by...