This monograph is devoted to the presidential election system in the United States, and to voting theory in general. In the first three chapters, the author offers mathematical models related to the three stages of the presidential elections in the USA (primaries, party conventions and the general election) and discusses the disadvantages of the Electoral College system. The other chapters deal with coalition politics, the Watergate scandal and a general comparison of voting systems (negative voting and approval voting). The models presented in the book employ only elementary probability theory and game theory. Most results are stated without proof but an extensive list of references is included. There is a wealth of examples from past US presidential elections.