The course of Automata, formal languages, computation and complexity is backbone of computer science; the mathematical preliminaries are the essential base and prerequisite for understanding of this course. This first chapter covers: Set operations, countable and uncountable sets, types of proofs, concept of solvability and unsolvability, computable and non-computable functions. Considering that many problems in computer science can be transformed into graphs—the platform from which solution can be more easily obtained using the graph algorithms, the chapter provides the coverage to essential part of graph theory. There is an analogy between models of computing machines and algebraic systems, and operations in algebra are isomorphic to those in these models, this has motivated to cover algebraic system in this chapter. Knowing that closure operation on strings is analogous to operations on languages, the operations on strings are presented, as well as the countable and uncountable languages. The chapter ends with self-review questions, followed with large number of classified exercises, and the references.