Neeman shares his research into proofs of determinacy for games of countable length, for readers with a knowledge of basic set theory, and some familiarity with Silver indiscernibles and extenders and iteration trees-all at a graduate level. He covers the basic components, games of fixed countable length, games of continuously coded length, pullbacks, when both players lose, along a single branch, and games that reach local cardinals. He appends a brief exposition of extenders, generic extensions, and iterability, but warns that it can serve better as a booster or reminder than as an initial exposure.