Cover -- Title -- Copyright -- Contents -- Introduction -- I: Mumford-Tate Groups -- I.A: Hodge structures -- I.B: Mumford-Tate groups -- I.C: Mixed Hodge structures and their Mumford-Tate groups -- II: Period Domains and Mumford-Tate Domains -- II.A: Period domains and their compact duals -- II.B: Mumford-Tate domains and their compact duals -- II.C: Noether-Lefschetz loci in period domains -- III: The Mumford-Tate Group of a Variation of Hodge Structure -- III.A: The structure theorem for variations of Hodge structures -- III.B: An application of Mumford-Tate groups -- III.C: Noether-Lefschetz loci and variations of Hodge structure -- IV: Hodge Representations and Hodge Domains -- IV.A: Part I: Hodge representations -- IV.B: The adjoint representation and characterization of which weights give faithful Hodge representations -- IV.C: Examples: The classical groups -- IV.D: Examples: The exceptional groups -- IV.E: Characterization of Mumford-Tate groups -- IV.F: Hodge domains -- IV.G: Mumford-Tate domains as particular homogeneous complex manifolds -- Appendix: Notation from the structure theory of semi-simple Lie algebras -- V: Hodge Structures with Complex Multiplication -- V.A: Oriented number fields -- V.B: Hodge structures with special endomorphisms -- V.C: A categorical equivalence -- V.D: Polarization and Mumford-Tate groups -- V.E: An extended example -- V.F: Proofs of Propositions V.D.4 and V.D.5 in the Galois case -- VI: Arithmetic Aspects of Mumford-Tate Domains -- VI.A: Groups stabilizing subsets of D -- VI.B: Decomposition of Noether-Lefschetz into Hodge orientations -- VI.C: Weyl groups and permutations of Hodge orientations -- VI.D: Galois groups and fields of definition -- Appendix: CM points in unitary Mumford-Tate domains -- VII: Classification of Mumford-Tate Subdomains -- VII.A: A general algorithm.

VII.B: Classification of some CM-Hodge structures -- VII.C: Determination of sub-Hodge-Lie-algebras -- VII.D: Existence of domains of type IV(f) -- VII.E: Characterization of domains of type IV(a) and IV(f) -- VII.F: Completion of the classification for weight 3 -- VII.G: The weight 1 case -- VII.H: Algebro-geometric examples for the Noether-Lefschetz-locus types -- VIII: Arithmetic of Period Maps of Geometric Origin -- VIII.A: Behavior of fields of definition under the period map - image and preimage -- VIII.B: Existence and density of CM points in motivic VHS -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W.