Chris Lintott, Professor of Astrophysics at the University of Oxford, lays out the case for cosmic inflation, the theory that the early universe expanded at a staggering rate in a fraction of a second. He builds up to it carefully, starting with Hubble's measurements of redshift and Cepheid variables, the cosmic microwave background, and the formation of helium in the universe's first three minutes. From there he explains the horizon problem, the flatness problem, and the missing magnetic monopoles that pushed Alan Guth toward his 'spectacular realization' in 1980. Lintott walks through how a region smaller than a pinhead could inflate to grapefruit size, covers the BICEP2 gravitational wave claim and its retraction, and closes on eternal inflation and the multiverse, using a block of cheese as an analogy. Delivered at Gresham College, this is a clear, well-paced survey of one of cosmology's stranger but best-evidenced ideas.