Monte-carlo simulation (Stochastic calculus)

Dear Experts,

I have reasonable understanding of Stochastic calculus by having gone through Book I and II by Steven Shreve.

I now plan to get an understanding of Monte-carlo simulation methodologies/techniques.

In this regard, Can I request the members in the forum to list a few books which are good to begin with.

I prefer a combination of books which are mathematically rigorous (my primary focus) and which will briefly state why a particular topic is being discussed.

Kindly guide me.

Thank you in advance for your help.