“If I want to understand something about invariants of finite groups, this is the book that I will go to, as I already have. … Overall this is an excellent book.” (Thomas Garrity, Mathematical Reviews, November, 2016)“The book under review is devoted to the constructive, algorithmic, approach to invariant theory. … The contents of the book under review can be divided in three parts. … it is so well structured that can be read by anyone with a basic background on algebraic groups.” (Felipe Zaldivar, MAA Reviews, maa.org, March, 2016)“This encyclopedic treatise gives a very comprehensive and lucid overview of the state of art in computational invariant theory and its applications, including numerous recent topics and results, and therefore it may serve as a highly useful source for advanced students and researchers in commutative algebra, algebraic geometry, computer algebra, group theory, discrete mathematics, information theory, computer science, and related fields of science.” (Werner Kleinert, zbMATH 1332.13001, 2016)

• Preface.- 1 Constructive Ideal Theory.- 2 Invariant Theory.- 3 Invariant Theory of Finite Groups.- 4 Invariant Theory of Reductive Groups.- 5 Applications of Invariant Theory.- A. Linear Algebraic Groups.- B. Is one of the two Orbits in the Closure of the Other? by V.L.Popov.- C. Stratification of the Nullcone by V.L.Popov.- Addendum to C. The Source Code of HNC by N.A’Campo and V.L.Popov.- Notation.- Index.

“If I want to understand something about invariants of finite groups, this is the book that I will go to, as I already have. … Overall this is an excellent book.” (Thomas Garrity, Mathematical Reviews, November, 2016)“The book under review is devoted to the constructive, algorithmic, approach to invariant theory. … The contents of the book under review can be divided in three parts. … it is so well structured that can be read by anyone with a basic background on algebraic groups.” (Felipe Zaldivar, MAA Reviews, maa.org, March, 2016)“This encyclopedic treatise gives a very comprehensive and lucid overview of the state of art in computational invariant theory and its applications, including numerous recent topics and results, and therefore it may serve as a highly useful source for advanced students and researchers in commutative algebra, algebraic geometry, computer algebra, group theory, discrete mathematics, information theory, computer science, and related fields of science.” (Werner Kleinert, zbMATH 1332.13001, 2016)

• Preface.- 1 Constructive Ideal Theory.- 2 Invariant Theory.- 3 Invariant Theory of Finite Groups.- 4 Invariant Theory of Reductive Groups.- 5 Applications of Invariant Theory.- A. Linear Algebraic Groups.- B. Is one of the two Orbits in the Closure of the Other? by V.L.Popov.- C. Stratification of the Nullcone by V.L.Popov.- Addendum to C. The Source Code of HNC by N.A’Campo and V.L.Popov.- Notation.- Index.

“If I want to understand something about invariants of finite groups, this is the book that I will go to, as I already have. … Overall this is an excellent book.” (Thomas Garrity, Mathematical Reviews, November, 2016)“The book under review is devoted to the constructive, algorithmic, approach to invariant theory. … The contents of the book under review can be divided in three parts. … it is so well structured that can be read by anyone with a basic background on algebraic groups.” (Felipe Zaldivar, MAA Reviews, maa.org, March, 2016)“This encyclopedic treatise gives a very comprehensive and lucid overview of the state of art in computational invariant theory and its applications, including numerous recent topics and results, and therefore it may serve as a highly useful source for advanced students and researchers in commutative algebra, algebraic geometry, computer algebra, group theory, discrete mathematics, information theory, computer science, and related fields of science.” (Werner Kleinert, zbMATH 1332.13001, 2016)

• Preface.- 1 Constructive Ideal Theory.- 2 Invariant Theory.- 3 Invariant Theory of Finite Groups.- 4 Invariant Theory of Reductive Groups.- 5 Applications of Invariant Theory.- A. Linear Algebraic Groups.- B. Is one of the two Orbits in the Closure of the Other? by V.L.Popov.- C. Stratification of the Nullcone by V.L.Popov.- Addendum to C. The Source Code of HNC by N.A’Campo and V.L.Popov.- Notation.- Index.