This monograph covers topics in the cohomology of monoids up through recent developments.  Jonathan Leech’s original monograph in the Memoirs of the American Mathematical Society dates back to 1975. This book is an organized, accessible, and self-contained account of this cohomology that includes more recent significant developments that were previously scattered among various publications, along with completely new material.  It summarizes the original Leech theory and provides a modern and thorough treatment of the cohomological classification of coextensions of both monoids and...