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Here we discuss inflation, a period of accelerated expansion that occurred in the very early history of the universe. We motivate inflation by describing the flatness and horizon problems, then explain how inflation resolves them. We describe the early history of inflationary ideas, then move on to modern work where we outline the standard scalar-field model for inflation, and define the slow-roll parameters that phenomenologically describe the dynamics of inflation. We briefly outline how inflation leads to the generation of density fluctuations in the universe; we mathematically describe the spectrum of these fluctuations, and confront it with modern observations. We end by discussing more speculative ideas in this area, including eternal inflation and multiverse.