Each of these books has great descriptions of the
material from the early weeks. Many of thm are out of print, but used copies are
so cheap and so high quality that it makes sense to buy them.
One place, which I mention without endorsing, is
Monte Carlo Methods, Hammersley, J M Handscomb, D C
This is the original book on Monte Carlo methods.
Much of the material is dated, but much of the dated material
should be known better than it is.
Monte Carlo Methods, Volume 1: Basics, Malvin Kalos, Paula Whitlock
A great gentle but consice and insightful introduction to Monte Carlo, particularly
for physical sciences.
The book is more mathematical than it pretends to be.
Monte Carlo theory, methods and examples, Art B. Owen
Still high quality and clear, but with more background and modern detail than the previous two.
Lots of careful and helpful practical examples from statistics.
Available only online, so far.
Importance Sampling: A Review, Surya T. Tokdar and Robert E. Kass
A statisticians' quick survey of importance sampling ideas, the relationship between
the basics and more advanced developments such as adaptively finding importance functions
and sequential importance sampling.