Introduction and Guide to the Handbook

This article discusses random matrix theory (RMT) in a nutshell — what it is about, what its main features are, and why it is so successful in applications. It first considers the simplest and maybe most frequently used standard example, the Gaussian Unitary Ensemble (GUE) of random matrices, before looking at several types of applications of RMT, focusing on random operators, counting devices, and RMT without matrices. It then provides a guide to the handbook, explaining how the other forty-two articles on mathematical properties and applications of random matrices are related and built one upon the other. It also lists some topics that are not covered in detail in the book and reviews recent new developments since the first edition of this handbook before concluding with a brief survey of the existing introductory literature.