This chapter provides more background material; its four sections present briefly what needs to be known about logic, category theory, point-set topology, and Boolean algebra. The first section reviews equational logic, model theory, and set theory. Terms and free algebras are built, and the basic properties of varieties are developed. The next section gives the notions needed from category theory, with few proofs. We head for adjunctions and equivalences between two categories. The third section sketches various kinds of topological spaces, including Boolean spaces, and new spaces are built out of old. Boolean algebras, in the last section, are important. They have a topological dual in Boolean spaces, created in two ways on prime ideals: the Stone topology through clopen sets, or equivalently the hull-kernel topology.