These notes serve as an introduction to "Commutative Algebra." They are aimed at students in the mathematics department who are familiar with the basic concepts of groups, rings, and fields as covered in the course "Elementary Algebra," and have been prepared to meet the needs of the undergraduate course "Commutative Algebra and Applications."

The material developed corresponds essentially to chapters 1-9 of the classic textbook by Atiyah and Macdonald, Introduction to Commutative Algebra. However, we have added elements of algebraic geometry and algebraic number theory, which are historically significant sources of "Commutative Algebra."

Special effort has been made to ensure that the central ideas of the 12 chapters and the proofs of the theorems are understandable by the student without requiring outside help. Thus, we have included everything necessary from algebra in chapter 0. Furthermore, the proofs are presented in full detail, which may contrast with the elegant brevity of the book by Atiyah and Macdonald.