Inflationary cosmology gives a very plausible explanation for many features of our universe, including its uniformity, itsmass density, and the patterns of the ripples that are observed in the cosmic microwave background. Most versions of inflation, however, imply that ouruniverse is not unique, but is part of a possibly infinite multiverse. The speaker will talk about how inflation works, and why he believes that the possibility of a multiverse should be taken seriously.