I. Singularity Theory.- Basic Properties of Complex Spaces and Germs.- Weierstrass Preparation and Finiteness Theorem.- Application to Analytic Algebras.- Complex Spaces.- Complex Space Germs and Singularities.- Finite Morphisms and Finite Coherence Theorem.- Applications of the Finite Coherence Theorem.- Finite Morphisms and Flatness.- Flat Morphisms and Fibres.- Singular Locus and Differential Forms.- Hypersurface Singularities.- Invariants of...