Conformal invariance in quantum field theory and statistical mechanics

The author presents an introducory overview of conformal invariance with special regards to the field theoretical interpretation and the formulation in terms of integrable statistical mechanics models. After an introduction to the connection of scale invariance and conformal invariance radical quantization, conformal families, the conformal algebra, and physical contraints some minimal models are presented. Then fusion rules and free massless boson and fermion fields are considered. Then after a description of the Coulomb-gas representation and Ginzburg-Landau theories the different statistical mechanics models are described. Then supersymmetric conformal theories, parafermionic theories, Wess-Zumnino-Witten models, coset space representations, and the Zamolodchikov C-theorem are described. (HSI)