1 Basic Notions Basic conventions and definitions of rings and algebras used in commutative algebra 2 Localization Localization of rings and modules and local ring construction 3 Properties of Localization Compatibility of localization with Hom and tensor, and local properties 4 Localization of Graded Rings Homogeneous localization of graded rings and graded modules 5 The Jordan-Hölder Theorem Uniqueness of composition series and well-definedness of length 6 Associated Primes Definitions and properties of prime avoidance and associated primes 7 Primary Decomposition Primary decomposition and uniqueness for modules over Noetherian rings 8 Integral Extensions Cayley-Hamilton theorem, integral elements, and integral extensions 9 Integral Extensions and Ideals Lying over and going up theorems for prime ideals in integral extensions 10 The Nullstellensatz Jacobson rings and the proof of the Hilbert Nullstellensatz 11 Blowup Algebras Blowup algebras and associated graded rings from an ideal 12 Flatness Definition of flat modules, characterization via Tor, and basic properties 13 Flatness and Localization A local criterion for flatness via checking at the maximal ideal 14 Completion Completion of rings and modules defined by filtrations 15 Properties of Completions Compatibility of completion with exact sequences, the Artin-Rees lemma 16 Krull Dimension Krull dimension via prime chains and its basic properties 17 System of Parameters Relationship between the system of parameters of a local ring and dimension 18 Fractional Ideals Fractional ideals, invertible modules, and the Picard group 19 Regular Local Rings Regular systems of parameters and characterizations of regular local rings 20 Divisors Cartier divisors and the class group in Dedekind domains 21 Noether Normalization Noether normalization theorem and applications for finitely generated algebras 22 Differentials Universal property of Kähler differentials and the naive cotangent complex