If you are interested in doing research in this field, you will want to learn of major applications, and for that purpose I could recommend the various chapters of The Oxford Handbook of Random Matrix Theory. The book is expensive, but many of the chapters are on arXiv. In particular, part III, includes a great number of applications.
Here is a list of 17 chapters from the Handbook on arXiv, in particular, including chapters on financial applications and on physics applications.