Contents -- Preface -- Applications of Reflection Amplitudes in Toda-Type Theories -- 1 Introduction -- 2 Normalization Factors and Reflection Amplitudes -- 3 Reflections of Zero-Modes -- 4 Quantization Conditions and Scaling Functions -- 5 Comparison with the TBA results -- 6 Vacuum expectation value of exponential operator -- Acknowledgement -- References -- Lax Pairs and Involutive Hamiltonians for CN and BCN Ruijsenaars-Schneider Models -- 1 Introduction -- 2 AN-1-type Ruijsenaars-Schneider model -- 3 Hamiltonian reduction of Cn and BCn RS models from AN-1-type ones -- 4 Lax representations and involutive Hamiltonians for Cn and BCn RS models -- 5 Degenerate cases -- 6 Nonrelativistic limit to the Calogero-Moser system -- 7 Summary and discussions -- Acknowledgement -- References -- Fateev's Models and Their Applications -- 1 Fateev's models -- 2 Thermodynamic Bethe Ansatz -- 3 Applications -- 4 Discussion -- References -- The ODE/IM Correspondence -- Introduction -- 1 Schrodinger equations -- 2 Functional relations in integrable models -- 3 The TQ/ODE connection -- 4 Generalisations -- 5 Duality and reduction -- 6 Conclusions -- Acknowledgements -- References -- Integrable Sigma Models -- 1 Introduction -- 2 The models -- 3 Theta terms and WZW terms -- 4 The particle content -- 5 The S matrices -- 6 Matching perturbative expansions -- 7 The free energy at finite temperature -- 8 Conclusion -- References -- Lorentz Lattice Gases and Spin Chains -- 1 Introduction -- 2 Integrable loop models and spin chains -- 3 Thermodynamic limit and finite-size behaviour -- 4 Concluding Remarks -- Acknowledgements -- References -- Quantum Calogero-Moser Models for Any Root System -- 1 Introduction -- 2 Quantum Calogero-Moser Models.

3 Coxeter invariant excited states triangularity and spectrum -- 4 Quantum Lax pair and quantum conserved quantities -- 5 Algebraic construction of excited states I -- 6 l operators -- 7 Algebraic construction of excited states II -- 8 Universal proof of involution of quantum conserved quantities for type I II and III models -- 9 Summary comments and outlook -- Acknowledgements -- References -- Quasi-Particles in Conformal Field Theories for Fractional Quantum Hall Systems -- 1 Summary of the lectures -- References -- Towards Form Factors in Finite Volume -- 1 Introduction. -- 2 The formulation of the problem. -- 3 The classical periodical problem for KdV. -- 4 Hamiltonian structure of finite-zone solutions. -- 5 Separation of variables. Baxter equation. -- 6 Quasi-classical wave functions and matrix elements. -- 7 Large L limit -- References -- Static and Dynamic Properties of Trapped Bose-Einstein Condensates -- 1 Introduction -- 2 Static Properties of Bose-Einstein Condensates -- 3 Collective Excitations and Stability of Two-Component Bose-Einstein Condensates -- 4 Dynamic Properties of Bose-Einstein Condensates -- Acknowledgment -- References -- Integrability of the Calogero Model: Conserved Quantities the Classical General Solution and the Quantum Orthogonal Basis -- 1 Introduction -- 2 Projection Method -- 3 Quantum Calogero Model -- 4 Quantum Calogero Model with Distinguishable Particles -- 5 Symmetrization of Non-symmetric Theory -- 6 Summary -- Acknowledgements -- References -- Conformal Boundary Conditions -- 0. Introduction -- 1. A lightning review of CFT -- 2. Boundary Conformal Field Theory -- 3. Boundary Operator Algebra -- 4. Integrable lattice models -- Acknowledgements -- References.