This is an English translation of the now classic "Algbre Locale - Multiplicits" originally published by Springer as LNM 11. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities. Many modifications to the original French text have been made for this English edition, making the text easier to read, without changing its intended informal character.

I. Prime Ideals and Localization.-
1. Notation and definitions.-
2. Nakayama's lemma.-
3. Localization.-
4. Noetherian rings and modules.-
5. Spectrum.-
6. The noetherian case.-
7. Associated prime ideals.-
8. Primary decompositions.- II. Tools.- A: Filtrations and Gradings.- B: Hilbert-Samuel Polynomials.- III. Dimension Theory.- A: Dimension of Integral Extensions.- B: Dimension in Noetherian Rings.- C: Normal Rings.- D: Polynomial Rings.- IV. Homological Dimension and Depth.- A: The Koszul Complex.- B: Cohen-Macaulay Modules.- C: Homological Dimension and Noetherian Modules.- D: Regular Rings.- Appendix I: Minimal Resolutions.- Appendix II: Positivity of Higher Euler-Poincaré Characteristics.- Appendix III: Graded-polynomial Algebras.- V. Multiplicities.- A: Multiplicity of a Module.- B: Intersection Multiplicity of Two Modules.- C: Connection with Algebraic Geometry.- Index of Notation.