In this paper, we systematically study the wellposedness, illposedness of the Hartree equation, and obtain the sharp local wellposedness, the global existence in H^s, s ≥ 1 and the small scattering result in H^s for 2 < γ < n and s ≥ \frac{γ}{2}-1. In addition, we study the nonexistence of nontrivial asymptotically free solutions of the Hartree equation.
