Mario Petrich received his Ph.D. from the University of Washington in 1961 and held positions in many universities across Austria, Canada, France, Germany, Italy, Portugal, Spain, the UK, and the US, including Pennsylvania State University, University of Western Ontario, University of Vienna, University of St Andrews, Simon Fraser University, and University of Montpellier. He was a founding editor of Semigroup Forum.Norman Reilly received his Ph.D. from Glasgow University in 1965 and has held positions at Glasgow University, Tulane University, and Simon Fraser University. Dr. Reilly has published over 100 articles and two books. He is a long time editor of Semigroup Forum and the International Journal of Algebra and Computation.

“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)

• Fully Invariant Relations.- Kernel and Trace Relations.- Bands.- Polák Theorem.