The recent development of theory on electron correlation in metals is explained in detail in this book. The strongest interaction between electrons in metals is the Coulomb repulsive force. This interaction gives rise to magnetism such as the ferromagnetism in Fe, Co and Ni. This interaction also induces the metal-insulator transition called the Mott transition. Surprisingly, recent studies confirm that the repulsive interaction is the origin of high temperature superconductivity in copper-oxide systems. Moreover, the number of new superconducting systems due to the electron correlation are rapidly increasing.