## ABSTRACT

We begin this chapter by introducing the mathematical notation and terminology used throughout the book. However, the focus of this chapter is concerned with abstract algebra, a subject not generally taught to engineering students. Comprehending abstract algebra is a necessity for understanding the discussion of lattice algebra in Chapter 3. The definitions and theorems of abstract algebra are based on the axioms of set theory. For this reason we start our discussion of abstract algebra by exploring the operations on sets, special sets used in other chapters, various functions on sets, as well as the notion of countable and uncountable sets. The discourse of abstract algebra ranges from groupoids and groups to rings and fields, and concludes with vector spaces and homomorphisms between algebraic systems.