Sets and set notations play an important role not only as a mathematical discipline but also as a tool to express mathematical ideas precisely. Here, we discuss some parts of set theory. Our primary use of sets is for communication purposes. In Sect. 1.1, we establish basic set theoretic notations and their use. In Sect. 1.2, we introduce counting principles and prove the binomial theorem which we use in subsequent chapters. Then we move to the introduction of functions in Sect. 1.3. The word “function” is used so frequently in mathematical courses that most feel comfortable with it, yet it is a word little understood. For example, from my experience, some students seem to have trouble understanding the difference between inverse of a function and inverse functions. So we practice set operations that involve functions. Then we move to mathematical induction in Sect. 1.4. Mathematical induction is another concept that many feel comfortable with, yet most mathematicians fail to communicate properly when using this method to write proofs. We reveal this “failure” in Sect. 1.4 by demonstrating the importance of quantifications.