**Tentative outline**

**1.** *Collective modes:* Hydrodynamic
limit; Importance of symmetries and dimensionality. Introduction to phase
transitions and critical phenomena.

**2.** *The Landau-Ginzburg model:* Mean-Field Theory;
Critical exponents; Goldstone modes and the Lower critical dimension; Fluctuations
and the Upper critical dimension.

**3.** *Universality:* Self-similarity; the Scaling
hypothesis; Kadanoff's heuristic Renormalization Group (RG), and exponent
identities.

**4.** *Perturbation theory:* Diagrammatic expansions;
Wilson's momentum space RG, and the taming of divergent perturbation series
by epsilon-expansions.

**5.** *Lattice models:* Ising, Potts, etc.; Position-space
RGs (cumulant, Migdal-Kadanoff); Monte-Carlo simulations; Finite-size scaling.

**6.** *Series expansions:* Low temperatures and
High temperatures; Duality; Random walk generating functions; Exact solution
of the two-dimensional Ising model.

**7.** *Two-dimensional films:* Algebraic order;
Topological defects; Melting and the Hexatic phase; the non-linear sigma model.

(If time permits, one of the following topics:)

**8.** *Dynamics:* Langevin equations; Conservation
laws; Dynamic universality classes.

**9.** *Random systems:* Annealed versus Quenched
impurities; Harris' Criterion; Random bonds; Random fields; Spin-glasses.

**10.** *Scaling theories of Polymers, and other networks*.