The concept of a set is one of the major scientific developments of the twentieth century. The level of rigor provided by the theory of sets ultimately led the modern mathematicians to discover fundamental notions such as the abstract groups and the topological spaces. A majority of ideas introduced in this chapter provide mathematical foundations to study important aspects of computer science such as related to data structures, algorithms, and programming. The main emphasis is to discuss some foundational tools needed to study certain important “configurations” and “processes” concerning the theory of computation. We also prove some useful theorems. The notations introduced in this chapter are used throughout the book.