1.    A review of thermodynamics and statistical mechanics
a.  Thermodynamics potentials and experimental observation
b.  Principals of statistical mechanics, microstates, ensembles, partition function
c.  Thermodynamics from statistical mechanics.
d.  Classical and quantum quantum limits.
e.  Interacting systems
     Some examples: magnets, fluids, liquid crystals, polymers and membranes.

2.    Phase transitions
a.   Symmetry breaking and competition between energy and entropy.
b.   Mean field theory – the Ising model, liquid crystals, Van der Waals fluid.
c.   Thermodynamics of phase transitions - 1st and 2nd order phase transitions.
d.   Landau theory of phase transitions. 
e.  The lower critical dimension for phase transitions.

3.    Response, correlations and fluctuations
a.  Susceptibility and correlations.
b.  Landau Ginzburg free energy functional G[m(r)].
c.  Correlation length and correlation functions

4.    Fluids in the Grand Canonical Ensemble.
a.    The chemical potential for the ideal gas and for interacting systems.
b.    Liquid-gas phase transition in the Van der Waals approximation.
c.    The density functional.

5.    Quantum  Systems.
a.    Introduction to the path integral method.
b.    The transverse field Ising model.
c.    Quantum phase transitions and quantum critical points.
d.    Quantum-classical crossover in an ideal gas.