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.