This proceedings volume covers the main fields of mathematics: analysis, algebra and number theory, geometry and topology, combinatorics and graphs, applied mathematics, numerical analysis and computer mathematics, probability and statistics, teaching and popularization of mathematics.

This volume presents introductory lectures on the Standard Model and Higgs physics, as well as QCD. These lectures provided the particle physics background for the main topics of the school: astroparticle physics and modern cosmology.

This advanced, accessible textbook on effective field theories uses worked examples to bring this important topic to a wider audience.

This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory. These include Hopf algebras underlying renormalization schemes in quantum field theory, noncommutative geometry with applications to index theory on one hand and the study of aperiodic solids on the other, geometry and topology of low dimensional manifolds with applications to topological field theory, Chern-Simons supergravity and the anti de Sitter/conformal field theory correspondence. It comprises seven lectures organized around three main topics, noncommutative geometry, topological field theory, followed by supergravity and string theory, complemented by some short communications by young participants of the school.

This volume outlines the status of fundamental physics at the threshold of the 21st century. Some of the world's leading theorists and experimentalists discuss ongoing research on the following topics: M Theory, Superstring Theory, Supersymmetry and Supergravity, Quantum Gravity, Dark Matter in the Universe, Gravitational Radiation, Proton Decay, Higgs Physics, Cosmology, Bose-Einstein Condensation.

This book provides an understanding of conformal field theory and its importance to both statistical mechanics and string theory. It introduces the Wess-Zumino-Novokov-Witten (WZNW) models and their current algebras, the affine Kac-Moody algebras.