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noncommutative geometry@n – the tools, contains the material a starting researcher needs to enter this fascinating new topic. Motivated by examples from representation theory of algebras, it initiates the reader to as different topics as : geometric invariant theory, etale cohomology, Brauer groups and rings satisfying polynomial identities. This volume contains the geometric reconstruction result for Cayley-Hamilton algebras, due to Claudio Procesi, and the etale local classification of Cayley-smooth algebras via marked quiver-settings. The second volume will focuss on applications to moduli spaces, quiver varieties and singularities. This is a two-year old preliminary version. An extended, updated and corrected version will appear in the fall of 2007 with Chapman&Hall. Use this version only for private use.