Lectures on conformal field theory and kac-moody algebras -- W-algebras and their representations -- Exact S-matrices -- to simple integrable models of quantum field theory -- to the coordinate-space bethe ansatz and to the treatment of bethe ansatz equations -- Thermodynamical bethe ansatz and condensed matter.

In the last few years we have witnessed an upsurge of interest in exactly solvable quantum field theoretical models in many branches of theoretical physics ranging from mathematical physics through high-energy physics to solid states. This book contains six pedagogically written articles meant as an introduction for graduate students to this fascinating area of mathematical physics. It leads them to the front line of present-day research. The topics include conformal field theory and W algebras, the special features of 2d scattering theory as embodied in the exact S matrices and the form factor studies built on them, the Yang--Baxter equations, and the various aspects of the Bethe Ansatz systems.