This monograph details several different methods for constructing simple relation algebras, many of which are new with this book. By drawing these seemingly different methods together, all are shown to be aspects of one general approach, for which several applications are given. These tools for constructing and analyzing relation algebras are of particular interest to mathematicians working in logic, algebraic logic, or universal algebra, but will also appeal to philosophers and theoretical computer scientists working in fields that use mathematics.

The book is written with a broad audience in mind and features a careful, pedagogical approach; an appendix contains the requisite background material in relation algebras. Over 400 exercises provide ample opportunities to engage with the material, making this a monograph equally appropriate for use in a special topics course or for independent study. Readers interested in pursuing an extended background study of relation algebras will find a comprehensive treatment in author Steven Givant’s textbook, Introduction to Relation Algebras (Springer, 2017).

Preface.- 1. Rectangular Semiproducts.- 2. Equivalence Semiproducts.- 3. Diagonal Semiproducts.- 4. Semipowers.- 5. Simple Closures.- 6. Quasi-bijective Relation Algebras.- 7. Quotient Relations Algebras and Equijections.- 8. Quotient Semiproducts.- 9. Group and Geometric Quotient Semiproducts.- 10. Insertion Semiproducts.- 11. Two-quasi-bijective Relation Algebras.- A. Relation Algebras.- B. Geometry.- C. Selected Hints to Exercises.- References.