Guide to Monte Carlo Methods?

I have started to realize that Monte Carlo methods of various kinds keep coming up in my work. Despite significant application of Monte Carlo in my grad school research, I think I only know enough to be dangerous. I’d like to get a better grasp on Monte Carlo methods (especially MCMC and simulation).

I asked on Twitter if anyone had a recommended reference that was readable and practical. Despite my love of measure theory, what I want is Monte Carlo Methods for the Very Applied Mathematician, not a theoretical text.

I got several recommendations. I’m not sure that any are exactly what I’m looking for, but I am certainly going to look deeper into them. Interestingly, they are all Springer books.

Several people recommended Glasserman’s Monte Carlo Methods in Financial Engineering. I don’t work in the financial sector, so it’s hard for me to evaluate the table of contents to tell how well it generalizes.

Someone else recommended both Explorations in Monte Carlo Methods and Handbook of Markov Chain Monte Carlo for two levels of MCMC.

Finally, I got a recommendation for Introducing Monte Carlo Methods with R. This might be closest to what I’m looking for. It appears to cover a breadth of topics, and it includes lots of code.