Random Matrix Theory comprises of some of the most beautiful ideas in modern day mathematics. Popularised extensively by the works of Eugene Wigner and Freeman Dyson in the 1950s (after being first used by John Wishart in mathematical statistics), the theory of random matrices has led insights into numerous fields (even those outside the realm of level statistics) in the last seven decades.
A good place to begin with Random Matrix Theory would be Bertrand Eynard’s lecture notes which can be found here. A classic book on the subject is Random Matrices by Madan Lal Mehta, widely considered the finest text introducing the theory.
I have been working my way through the theory of random matrices for quite some time now and plan to put more posts on the topic up here in the future.