There's an excellent account by Nadeem Rezavi which you can read here if you have access to JSTOR. If you don't have access, you can still read it by signing up for a free account, which permits you to read a limited number of articles per month.

If you are looking for primary sources, you should start with the Ain-i-Akbari written by Abul Fazal. You can find the full text at archive.org, here. It goes into detail about the schools and universities set up by Akbar, which combined Arab, Persian and Sanskrit texts to provide a comprehensive secular education.

Another source is François Bernier's Travels in the Mogul Empire A.D. 1656–1668. You can read the full text at Columbia University's website here.

Specifically on Muslim education, you may want to read The Dabistan or "School of Manners" by David Shea. You can read the full text at archive.org here. And here's Volume 2.

There's this bit about Ponnani in North Kerala's Mallapuram district, in the region known as Malabar. The town's Juma Masjid was often regarded as the Mecca of Malabar. [It attracted students from far flung regions such as Sumatra and Java.](https://books.google.co.in/books? []id=OM5TDwAAQBAJ&pg=PA119&dq=mecca+of+malabar+java&hl=en&sa=X&ved=0ahUKEwiHjPTyhajhAhXR73MBHTxKCk4Q6AEILjAB#v=onepage&q=Mecca%20of%20malabar%20&f=false) [pg119, last para.]

South India's traders were crucial in the spread of not just Hindu and Buddhist ideas in Nusantara , but also Islamic theology.

Edit: Islam in South East Asia. It's a short read.

u/ayr909: I think you'd have more to say.