1．The One-Dimensional Quantum Spin Chain 1
1.1 The S=1/2 XXZ Spin Chain 1
1.2 The Jordan-Wigner Transformation and the Quantum Kink 7
1.3 The Bethe Ansatz and the Exact Solution 11
2．Quantum Field Theory in 1+1 Dimensions 23
2.1 Bosonization 23
2.2 Conformal Field Theory 45
2.3 The Non-linear Sigma Model 63
3．Strongly Correlated Electronic Systems 73
3.1 Models of Strongly Correlated Electronic Systems 73
3.2 Spin-Charge Separation in One Dimension 82
3.3 Magnetic Ordering in Strongly Correlated Electronic Systems 89
3.4 Self-consistent Renormalization Theory 98
4．Local Electron Correlation 117
4.1 The Kondo Effect 117
4.2 Dynamical Mean Field Theory 134
5．Gauge Theory of Strongly Correlated Electronic Systems 139
5.1 Gauge Theory of Quantum Anti-ferromagnets 139
5.2 Gauge Theory of the Doped Mott Insulator 142
5.3 Gauge Theory of Quantum Hall Liquids 152
Appendix 159
A．Complex Functions 159
A.1 Projection from the z-Plane to the w-Plane 160
A.2 Contour Integral of f(z) Around the Path C 160
B．The Variational Principle and the Energy-Momentum Tensor 161
Literature 165
Index 169