I. Hodge structures attached to primitive forms of weight 2 -- 0. Definitions and notations -- 1. Hodge structures attached to Hilbert modular surfaces -- 2. Hodge structures attached to primitive forms of weight 2 -- 3. Nonholomorphic involutive automorphisms of Hilbert modular surfaces -- 4. Period relation of Riemann-Hodge -- II. Abelian varieties attached to primitive forms -- 5. Abelian varieties attached to Clifford algebras -- 6. The period moduli of the isogeny classes Atf ? Q and A2f ? Q -- 7. Main theorem A and its corollaries -- 8. Selfconjugate forms and algebraic cycles -- 9. Abelian varieties attached to non-selfconjugate forms -- III. Correspondence between real Nebentype elliptic modular forms and Hilbert modular forms -- 10. Weil representation and theta series -- 11. Construction of real Nebentype elliptic modular forms -- 12. Construction of Hilbert modular forms -- 13. The adjointness formula -- IV. Period relation for the lifting of modular forms and transcendental cycles -- 14. Hodge structures attached to real Nebentype elliptic modular forms of weight 2 -- 15. Construction of 2-cycles -- 16. Arithmetic index theorems -- 17. Period relation for the Doi-Naganuma lifting and Main Theorem B -- 18. Selfconjugate forms and transcendental cycles -- 19. Notes on ?-adic cohomology groups of certain Hilbert modular surfaces -- 20. Remarks -- Bibliography.