1. 1+1 DIMENSIONAL INTEGRABLE SYSTEMS
1.1 KdV equation, MKdV equation and their Darboux transformations
1.2 AKNS system
1.3 Darboux transformation
1.4 KdV hierarchy, MKdV-SG hierarchy, NLS hierarchy and AKNS system with u(N) reduction
1.5 Darboux transformation and scattering, inverse scattering theory

2. 2+1 DIMENSIONAL INTEGRABLE SYSTEMS
2.1 KP equation and its Darboux transformation
2.2 2+1 dimensional AKNS system and DS equation
2.3 Darboux transformation
2.4 Darboux transformation and binary Darboux transformation for DS equation

3. N+1 DIMENSIONAL INTEGRABLE SYSTEMS
3.1 n+1 dimensional AKNS system
3.2 Darboux transformation and soliton solutions
3.3 A reduced system on Rⁿ

4. SURFACES OF CONSTANT CURVATURE, BACKLUND CONGRUENCES
4.1 Theory of surfaces in the Euclidean space R³
4.2 Surfaces of constant negative Gauss curvature, sine-Gordon equation and Backlund transformations
4.3 Surface of constant Gauss curvature in the Minkowski space R^2,1 and pseudo-spherical congruence
4.4 Orthogonal frame and Lax pair
4.5 Surface of constant mean curvature

5. DARBOUX TRANSFORMATION AND HARMONIC MAP
5.1 Definition of harmonic map and basic equations
5.2 Harmonic maps from R² or R^1,1 to S², H² or S^1,1
5.3 Harmonic maps from R^1,1 to U(N)
5.4 Harmonic maps from R² to U(N)

6. GENERALIZED SELF-DUAL YANG-MILLS AND YANG-MILLS-HIGGS EQUATIONS
6.1 Generalized self-dual Yang-Mills flow
6.2 Yang-Mills-Higgs field in 2+1 dimensional Minkowski space-time
6.3 Yang-Mills-Higgs field in 2+1 dimensional anti-de Sitter space-time

7. TWO DIMENSIONAL TODA EQUATIONS AND LAPLACE SEQUENCES OF SURFACES
7.1 Signed Toda equations
7.2 Laplace sequences of surfaces in projective space P^n-1
7.3 Darboux transformation
7.4 Su chain (Finikoff configuration)
7.5 Elliptic version of Laplace sequence of surfaces in CPⁿ

Contents, Chapter1 and Chapter 2

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