- Plane curves
- Manifolds and varieties via sheaves
- More sheaf theory
- Sheaf cohomology
- De Rham cohomology of manifolds
- Riemann surfaces
- Simplicial methods
- The Hodge theorem for Riemannian manifolds
- Toward Hodge theory for complex manifolds
- Kahler manifolds
- A little algebraic surface theory
- Hodge structures and homological methods
- Topology of families
- The hard Lefschetz theorem
- Coherent sheaves
- Cohomology of coherent sheaves
- Computations of some Hodge numbers
- Deformations and Hodge theory
- Analogies and conjectures

- p. 164. l.10 from the bottom: The definition of the approximate heat kernel \(K_0\) is wrong as written. There should be an extra cutoff factor: \[K_0(x,y,t) = (4 \pi t)^{-n/2} e^{-\delta(x,y)^2/4t}\delta(x,y)^2\] so that it dies off away from the diagonal.
- p.180, l.1: the 2nd and 4th _i should be _j
- p.180, l.4: at the end of the line "(X)" should be "_X"
- p.184, l.13: the third \(\partial\) should be \(\bar\partial\) and the third \(\bar\partial\) should be \(\partial\)
- p.185, displayed line in 10.2.6: second "q" should be "p", first "_Y" should be "_X"
- p.204: in the definition of a pure Hodge structure there is no \(H_{\mathbb C}\), just an H. Then in two displayed equations on this page it appears.
- p.204, l.18: \(H^{pq}\) should be \(H^{p'q}\)
- pp.203-205: There is some inconsistency about the symbol H. It should stand for the complex vector space and \(H_{ \mathbb{Z}}\) for the lattice.
- p.205, l.5: in the definition of a direct sum of Hodge structures. There shouldn't be a sum on the right side.
- p.208, l.12: \(\mathcal{H}\) should be regular \(H\).
- p.208, l.13-14: "I think here the superscript of the curly H''s should be p+q instead of q, because the Gr^p's are supported at the p^th term, so you get a shift in cohomology."
- p.208, end of proof of 12.2.4: something like "by Lemma 12.1.1" should be added.
- p.214,l.1: ^p should be ^i
- p 215, 12.4.6: it should read "\(< \infty\)"
- p 221, l4, should be "Carlson"