These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories.

An attempt to unify fundamental interactions by assuming that physical spacetimes can be regarded as submanifolds of certain 8-dimensional space. Book in PDF by Matti Pitkänen, Helsinki.

A brief introduction to Topological Quantum Field Theory as well as a description of recent progress made in the field is presented. I concentrate mainly on the connection between Chern-Simons gauge theory and Vassiliev invariants, and Donaldson theory and its generalizations and Seiberg-Witten invariants. Emphasis is made on the usefulness of these relations to obtain explicit expressions for topological invariants, and on the universal structure underlying both systems.

A topological quantum field theory (TQFT) is an, almost, metric independent quantum field theory that gives rise to topological invariants of the background manifold

Topological quantum field theories can be used as a powerful tool to probe geometry and topology in low dimensions. Chern-Simons theories, which are examples of such field theories, provide a field theoretic framework for the study of knots and links in three dimensions.

Research Group on Topological Quantum Field Theories in any dimension and their relation to topological invariants. Particular attention is given to BF theories and knots in any dimension.

Includes links to research papers, quotations on the development of the quantum theory, brief notes on the field and related links.

A brief review on some of the recent developments in topological quantum field theory. These include topological string theory, topological Yang-Mills theory and Chern-Simons gauge theory.