This is an introductory textbook that introduces concepts in set theory that all students must know. The construction of various number systems and the real number system with the help of Dedekind cut approach are provided. The properties of the real number system are given in detail. The equivalent statements of the Axiom of Choice are given and the equivalence is proved. A surprising consequence of the Axiom of Choice is discussed in the book. The detailed properties of the ordinals and the cardinals are also discussed. At the end an appendix is added which counts the number of elements in various important finite sets.