Table of Contents

I Noncommutative affine schemes.- II The left spectrum and irreducible representations of ‘small’ quantized and classical rings.- III Noncommutative local algebra.- IV Noncommutative local algebra and representations of certain rings of mathematical physics.- V Skew PBW monads and representations.- VI Six spectra and two dimensions of an abelian category.- VII Noncommutative Projective Spectrum.- Reference.- Index of Notations.