This book introduces aspects of topology and applications to problems in condensed matter physics. Basic topics in mathematics have been introduced in a form accessible to physicists, and the use of topology in quantum, statistical and solid state physics has been developed with an emphasis on pedagogy. The aim is to bridge the language barrier between physics and mathematics, as well as the different specializations in physics. Pitched at the level of a graduate student of physics, this book does not assume any additional knowledge of mathematics or physics. It is therefore suited for advanced postgraduate students as well. A collection of selected problems will help the reader learn the topics on one's own, and the broad range of topics covered will make the text a valuable resource for practising researchers in the field. The book consists of two parts: one corresponds to developing the necessary mathematics and the other discusses applications to physical problems. The section on mathematics is a quick, but more-or-less complete, review of topology. The focus is on explaining fundamental concepts rather than dwelling on details of proofs while retaining the mathematical flavour. There is an overview chapter at the beginning and a recapitulation chapter on group theory. The physics section starts with an introduction and then goes on to topics in quantum mechanics, statistical mechanics of polymers, knots, and vertex models, solid state physics, exotic excitations such as Dirac quasiparticles, Majorana modes, Abelian and non-Abelian anyons. Quantum spin liquids and quantum information-processing are also covered in some detail.

The proceedings of this workshop contains 5 important papers by S A Edwards on the Edwards Model and includes discussions on recent theoretical developments in polymer physics.A few decades ago, polymers were not considered part of conventional physics. However, the scenario changed drastically in the sixties and seventies with the introduction of path integral methods, fields theory in the n limits, and renormalization group approach. A vital step in this progress is the path integral Hamiltonian that S F Edwards proposed in 1965-66 to study a single chain. This model now called the Edwards model, is considered to be the minimal model for polymers, and it has been phenomenal in unraveling the universal properties of polymers, be it a single chain or many, equilibrium or dynamics. It has now crossed the boundary of polymers and is finding applications through appropriate generalizations in many other problems.