Local Algebra

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This is an English translation of the now classic Algebre Locale - Multiplicites originally published by Springer as LNM 11, in several editions since 1965. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities ( Tor-formula ). Many modifications to the original French text have been made by the author for this English edition: they make the text easier to read, without changing its intended informal character.