This book is a unified treatment of the most important core developments in the theory of completely regular semigroup theory as it stands today. This volume focuses on the lattice of varieties of completely regular semigroups. Since any in-depth study of the lattice of varieties requires an understanding of free completely regular semigroups, the book begins by describing the free object on countably infinite sets and the properties of the lattice of fully invariant congruences on the free object. The authors introduce various associated relations and operators on the lattice of varieties of completely regular semigroups. Following that, the book covers the sublattice of varieties of bands with a focus on the influence of that sublattice on the structure of the whole lattice. The book concludes with the remarkable theorem due to Polák describing the whole lattice of varieties of completely regular as a subdirect product of lattices,some of which are well understood. The authors include recent advances, insights, results, and techniques throughout the book.

"Current advancements with their insights, related recent results and their methodologies etc. are nicely and elaborately included in this book and some of which are enlighted with in-depth understanding and special mention of the whole lattice of varieties of completely regular as a subdirect product of lattices which is in fact a remarkable theorem due to Pola'k. The book consists of an insightful and resourceful bibliography at the end." (Sanjib Kumar Datta, zbMATH 1545.20001, 2024)