Research on electronic systems in condensed matter physics is at present developing very rapidly, where the main focus is changing from the ”single-particle problem” to the ”many-particle problem”. That is, the main research interest changed from phenomena that can be understood in the single particle picture, as, for example, in band theory, to phenomena that arise owing to the interaction between many electrons.

1. The One-Dimensional Quantum Spin Chain1.1 The S = 1/2 XXZ Spin Chain1.2 The Jordan-Wigner Transformation and the Quantum Kink 1.3 The Bethe Ansatz and the Exact Solution2. Quantum Field Theory in 1+1 Dimensions 2.1 Bosonization2.2 Conformal Field Theory2.3 The Non-linear Sigma Model3. Strongly Correlated Electronic Systems3.1 Models of Strongly Correlated Electronic Systems3.2 Spin-Charge Separation in One Dimension3.3 Magnetic Ordering in Strongly Correlated Electronic Systems3.4 Self-consistent Renormalization Theory4. Local Electron Correlation4.1 The Kondo Effect4.2 Dynamical Mean Field Theory 5. Gauge Theory of Strongly Correlated Electronic Systems.5.1 Gauge Theory of Quantum Anti-ferromagnets5.2 Gauge Theory of the Doped Mott Insulator5.3 Gauge Theory of Quantum Hall Liquids AppendixA. Complex FunctionsA.1 Projection from the z-Plane to the w-PlaneA.2 Contour Integral of f(z) Around the Path CB. The Variational Principle and the Energy-Momentum TensorLiteratureIndex