You can find many websites about the Mamluk Sultanate and the Middle-East on the Internet. I don't want to copy here the important dates, the list of sultans, etc. If you are interested in Mamluk reenactment I suppose you are a bit familiar with middle-eastern warfare.
If You want to reenact a mamluk or other middle-eastern warrior, I would recommend one book: The Crusades Through Arab Eyes by Amin Maalouf. It is composed using contemporary sources, and the great thing is that the author used Arab chronicles, not Western sources as in most books about the crusades. Thus this book is really good regarding the history, politics and everyday life of the Middle-East in the middle ages.