Swanson I., Huneke C. Integral Closure of Ideals, Rings, and Modules

Cambridge: Cambridge University Press, 2015. — 454 p.This is a graduate-level textbook, and it is also meant to be a reference for researchers. We assume some basic background in commutative algebra, such as completions.What is integral closure of ideals?
Integral closure of rings
Separability
Noetherian rings
Rees algebras
Valuations
Derivations
Reductions
Analytically unramified rings
Rees valuations
Multiplicity and integral closure
The conductor
The Briancon-Skoda Theorem
Two-dimensional regular local rings
Computing integral closure
Integral dependence of modules
Joint reductions
Adjoints of ideals
Normal homomorphisms
Appendix A Some background material
Some forms of prime avoidance; Caratheodory's theorem; Grading; Complexes; Macaulay representation of numbers
Appendix B Height and dimension formulas
Going-Down, Lying-Over, flatness; Dimension and height inequalities; Dimension formula; Formal equidimensionality; Dimension Formula