part I Classical Hodge theory -- chapter 1 Spectral sequences and mixed Hodge structures -- chapter 2 Complex manifolds, vector bundles, differential forms -- chapter 3 Sheaves and cohomology -- chapter 4 Harmonic forms on hermitian manifolds -- chapter 5 Hodge theory on compact ka¨hlerian manifolds -- chapter 6 The theory of residues on a smooth divisor -- chapter 7 Complex spaces -- part II Differential forms on complex spaces -- chapter 1 The basic example -- chapter 2 Differential forms on complex spaces -- chapter 3 Mixed Hodge structures on compact spaces -- part III Mixed Hodge structures on noncompact spaces -- chapter 1 Residues and Hodge mixed structures: Leray theory -- chapter 2 Residues and mixed Hodge structures on noncompact mani- folds -- chapter 3 Mixed Hodge structures on noncompact spaces: the basic example -- chapter 4 Mixed Hodge structures on noncompact singular spaces.