What background is required to understand Random Matrix Theory I would like to grasp RMT. I have knowledge on


*

*linear algebra, 

*classical probability theory,


Despite the above ones what should I study to understand RMT? Where to start? Is there any beginner's guide?
 A: Depending on what is your current level of maths education,
I think that reading research papers to introduce yourself to the theory of random matrices (i.e. to get what it's all about) is perhaps not the best strategy,
especially given the abundance of books/lecture notes on the subject (which usually give a much more accessible treatment of the theory).
My advice to you will depend on what you mean exactly by "understand RMT".

1. If you mean being able to follow and understand the demonstrations of classical results in the theory,
such as Wigner's semicircle law or the Marchenko-Pastur law,
then you will need the following background:


*

*Undergraduate linear algebra (ex. the spectral theorem,
relationship between the trace and the eigenvalues of normal matrices,...)

*Undergraduate combinatorics/discrete mathematics (ex. catalan numbers, graphs, Dyck paths,...)

*And most importantly, graduate level probability theory/measure theory (ex. convergence of probability measures (weak, in probability, almost sure), method of moments,...)


To acquire this knowledge,
I recommend looking at the book spitfiredd recommended in his comment (which is an excellent book).
From page 1 to 105,
the author (T. Tao) introduces the necessary background in probability and linear algebra to understand the rest of his book.
If you find that reading this background is too hard,
then I recommend you first take graduate courses in measure theory and probability,
and then try to read the introduction to T. Tao's book again.
Once you have the necessary background,
instead of trying to read research articles on random matrix theory,
I recommend you read one of (or parts of several of)


*

*Topics in Random Matrix Theory by T. Tao;

*An introduction to random matrices;

*Spectral Analysis of Large Dimensional Random Matrices.


In fact,
these books probably contain many of the results you were reading about in the papers you mentioned (unless what you were reading was really cutting edge) presented in a much more accessible way.

If you mean having a more conceptual understanding of the theory of random matrices,
such as understanding the motivations for studying certain aspects of random matrices or what makes certain results/open problems interesting,
then a good place to start would be to study the applications of random matrices in physics, statistics, pure mathematics, etc.
For this I recommend the first sections in Random Matrices by Mehta,
or chapters 24-43 of the Oxford Handbook of Random Matrix Theory (many of these chapters on applications can be hard to read, but they include lots of useful references).

Also, see this stackexchange question for other references.
