Random matrix theory plays a central role in statistical physics, computational mathematics and engineering sciences, including data assimilation, signal processing, combinatorial optimization, compressed sensing, econometrics and mathematical finance, among numerous others. The mathematical foundations of the theory of random matrices are technical, and mathematically difficult to penetrate for non-experts, regular users and practitioners. This book reviews and extends some important results in random matrix theory in the specific context of real random Wishart matrices. To overcome the complexity of the subject matter, the authors use a lecture note style to make the material accessible to a wide audience. This results in a comprehensive and self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition of Wishart matrix moments. All researchers and students requiring an accessible introduction to the topic will find this book essential reading.