Monte Carlo methods are computational techniques that use random sampling. Nicholas Metropolis and Stanislaw Ulam, both working for the Manhattan Project at the Los Alamos National Laboratory in the 1940s, first developed and used these methods. Ulam, who is known for designing the hydrogen bomb with Edward Teller, invented the method inspired, in his own words, “… by a question which occurred to me in 1946 as I was convalescing from an illness and playing solitaires. The question was what are the chances that a Canfield solitaire laid out with 52 cards will come out successfully?”. This was a new era of digital computers, and the answer Ulam gave involved generating many random numbers in a digital computer.

Metropolis and Ulam soon realized they could apply this method of successive random operations to physical problems, such as the one of neutron diffusion or the statistical calculation of volumetric properties of matter. Metropolis coined the term “Monte Carlo” in reference to the famous casino in Monte Carlo, Monaco, and the random processes in card games. Arguably, this is the most successful name ever given to a mathematical algorithm.

Nowadays Monte Carlo refers to very many different methods with a wide spectrum of applications. We present the Metropolis Monte Carlo method for sampling the phase space to compute ensemble averages, although often we only use the term “Monte Carlo” in subsequent discussions.