Theoretical studies will be conducted on the physics of two outstanding problems relating to high temperature superconductors - the anomalous superconducting fluctuations and the strong electron correlation problem. In particular, detailed calculations will be done to improve our understanding of the ground state of the superconducting oxides in a magnetic field. Further work will be conducted on the mechanism driving the superconductivity and the nature of the pairing, as well as the anomalous properties of the normal state.