1. Introduction
2. The Hubbard Hamiltonian and its symmetries
3. The Bethe ansatz solution
4. String hypothesis
5. Thermodynamics in the Yang-Yang approach
6. Ground state properties in the thermodynamic limit
7. Excited states at zero temperature
8. Finite size corrections at zero temperature
9. Asymptotics of correlation functions
10. Scaling and continuum limits at half-filling
11. Universal correlations at low density
12. The algebraic approach to the Hubbard model
13. The path integral approach to thermodynamics
14. The Yangian symmetry of the Hubbard model
15. S-matrix and Yangian symmetry in the infinite interval limit
16. Hubbard model in the attractive case
17. Mathematical appendices.

This book presents an account of the exact solution of the Hubbard model in one dimension. The early chapters develop a self-contained introduction to Bethe's ansatz and its application to the one-dimensional Hubbard model. The later chapters address more advanced topics.