Ideas from the theory of critical phenomena have been of great importance in the modelling of polymers ever since the Nobel prize winner P. G. de Gennes showed (in 1972) how the two subjects can be connected. In the 25 years that have passed since then, almost every major development in the understanding of criticality has led to parallel progress in the study of polymer models. We can think of the renormalisation group, the introduction of ideas from fractal geometry, conformal invariance …. As a result of all this work, the equilibrium behaviour of a polymer in a diluted regime is by now very well understood. That's why I considered the time ripe to write an overview of this field of research.

There already exist excellent books on the statistical mechanics of polymers and it may therefore be important to say a few words about the ‘niche’ in which this book should be placed. I have put the emphasis on models on a lattice and have therefore said very little about models, and methods to treat them, which work in the continuum. For completeness, important results obtained in the continuum are mentioned, but it would take much more space (and expertise on the part of the author) to treat them in all detail. Moreover, they have been very well described, for example in. This book also deals almost exclusively with the very dilute regime in which we can study one isolated polymer and can neglect the influence of any other polymers which may be present.