1. Thermodynamical Bethe Ansatz (TBA)
2. Lattice Path Integral Formulation and Quantum Transfer Matrix (QTM)
3. Fusion Algebra: T- and Y-Systems
4. Non-Linear Integral Equations
5. Higher Rank Models and Continuum Systems

The main topic of my lectures will be the finite temperature physics of integrable 1d quantum systems. The discussion will be rather comprehensive and detailed for the case of the spin-1/2 Heisenberg chain, but not restricted to this.
In the first lecture I will discuss the combinatorial TBA method introduced by Yang and Yang for the single component Bose gas and generalized by Gaudin and Takahashi to the Heisenberg chain.
Lectures 2 and 3 are devoted to an algebraic approach to the thermodynamical properties of integrable quantum chains. The finite temperature systems are mapped to classical models on 2d lattices. The partition function is obtained from just the largest eigenvalue of the column-to-column transfer matrix, also called the quantum transfer matrix which acts in an infinite dimensional space. A hierarchy of transfer matrices is derived by the fusion method, and algebraic relations of various type are established.
Lecture 4: By use of the so-called T- and Y-systems
(i) the TBA equations are derived rigorously,
(ii) alternative, especially finite sets of non-linear integral equations are derived,
(iii) correlation lengths/mass gaps are calculated.
In Lecture 5 generalizations to higher rank models and continuum limits like Bose gases are discussed.