Quantum Stochastic Calculus and Representations of Lie Superalgebras This book describes the representations of Lie superalgebras that are yielded by a graded version of Hudson Parthasarathy quantum stochastic calculus. Quantum stochastic calculus and grading theory are given concise introductions extending readership to mathematicians and physicists with a basic knowledge of algebra and infinite dimensional Hilbert spaces. The develpment of an explicit formula for the chaotic expansion of a polynomial of quantum stochastic integrals is particularly interesting. The book aims to provide a self contained exposition of what is known about Z_2 graded quantum stochastic calculus and to provide a framework for future research into this new and fertile area