Acknowledgements
Introduction
Relationship Chart
Chapter 0.A Prehistory of Tight Closure
Chapter 1.Basic Notions
Chapter 2.Test Elements and the Persistence of Tight Closure
Chapter 3.Colon-Capturing and Direct Summands of Regular Rings
Chapter 4.F-Rational Rings and Rational Singularities
Chapter 5.Integral Closure and Tight Closure
Chapter 6.The Hilbert-Kunz Multiplicity
Chapter 7.Big Cohen-Macaulay Algebras
Chapter 8.Big Cohen-Macaulay Algebras Ⅱ
Chapter 9.Applications of Big Cohen-Macaulay Algebras
Chapter 10.Phantom Homology
Chapter 11.Uniform Artin-Rees Theorems
Chapter 12.The Localization Problem
Chapter 13.Regular Base Change
Appendix 1: The Notion of Tight Closure in Equal Characteristic Zero (by M.Hochster)
Appendix 2: Solutions to the Exercises
Bibliography
