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Provides a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of $mtimes m$ matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation.

Features proceedings that contain the contributions of some of the participants in the "intensive research period" held at the De Giorgi Research Center in Pisa, during the period May-June 2010.