Introduction to Modern Set Theory is designed for aone-semester course in set theory at the advanced undergraduate or beginning graduate level. Three features are the full integration into the text of the study of models of set theory, the use of illustrative examples both in the text and in the exercises, and the integration of consistency results and large cardinals into the text early on. This book is aimed at two audiences: studentswho are interested in studying set theory for its own sake, and studentsin other areas who may be curious about applications of set theory totheir field. In particular, great care is taken to develop the intuitions thatlie behind modern, as well as classical, set theory, and to connect settheory with the rest of mathematics.