Includes bibliographical references.

Filtrations on the cohomology of abelian varieties ; Building mixed Hodge structures ; The Atiyah-Chern character yields the semiregularity map as well as the infinitesimal Abel-Jacobi map ; Regulators and characteristic classes of flat bundles ; Height pairings asymptotics and Bott-Chern forms ; Logarithmic Hodge structures and classifying spaces ; Motives and algebraic de Rham cohomology ; Hermitian vector bundles and characteristic classes ; The mixed motive of a projective variety ; Bloch's conjecture and the theory of projective surfaces ; From Jacobians to one-motives: Exposition of a conjecture of Deligne ; Motives, algebraic cycles and Hodge theory ; Picard-Fuchs uniformization: Modularity of the mirror map and mirror-moonshine ; Hilbert modular varieties in positive characteristic ; On the Neron-Severi groups of some surfaces ; Torsion zero-cycles and the Abel-Jacobi map over the real numbers ; A remark on the Griffiths groups of certain product varieties ; adic Abel-Jacobi maps and adic heights ; Crystalline fundamental groups and adic Hodge theory ; Thompson series, and the mirror maps of pencils of surfaces