From Kondo Effect to Fermi Liquid

The Kondo effect has been playing an important role in strongly correlated electon systems. The important point is that the magnetic impurity in metals is a typical example of the Fermi liquid. In the system the local spin is conserved in the ground state and continuity with respect to Coulomb repulsion $U$ is satisfied. This nature is satisfied also in the periodic systems as far as the systems remain as the Fermi liquid. This property of the Fermi liquid is essential to understand the cuprate high-Tc superconductors (HTSC). On the basis of the Fermi liquid theory we develop the transport theory such as the resistivity and the Hall coefficient in strongly correlated electron systems, such as HTSC, organic metals and heavy Fermion systems. The significant role of the vertex corrections for total charge- and heat-currents on the transport phenomena is explained. By taking the effect of the current vertex corrections into account, various typical non-Fermi-liquid-like transport phenomena in systems with strong magnetic and/or superconducting flucutations are explained within the Fermi liquid theory.