This book describes the representations of Lie superalgebras that are yielded by a graded version of Hudson-Parthasarathy quantum shastic calculus. Quantum shastic 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 shastic integrals is particularly interesting. The book aims to provide a self-contained exposition of what is known about Z_2-graded quantum shastic calculus and to provide a framework for future research into this new and fertile area.