§16§Properties of systems with long range interactions are still poorly understood despite being of importance in most areas of physics. The present volume introduces and reviews the effort of constructing a coherent thermodynamic treatment of such systems by combining tools from statistical mechanics with concepts and methods from dynamical systems. Analogies and differences between various systems are examined by considering a large range of applications, with emphasis on Bose--Einstein condensates. Written as a set of tutorial reviews, the book will be useful for both the experienced researcher as well as the nonexpert scientist or postgraduate student. §04§Dynamics and Thermodynamics of Systems with Long-Range Interactions: An Introduction.- Dynamics and Thermodynamics of Systems with Long-Range Interactions: An Introduction.- Statistical Mechanics.- Thermo-statistics or Topology of the Microcanonical Entropy Surface.- Ensemble Inequivalence in Mean-Field Models of Magnetism.- Phase Transitions in Finite Systems.- Phase Transitions in Systems with 1/r ? Attractive Interactions.- Nonextensivity: From Low-Dimensional Maps to Hamiltonian Systems.- Astrophysics.- Statistical Mechanics of Gravitating Systems in Static and Cosmological Backgrounds.- Statistical Mechanics of Two-Dimensional Vortices and Stellar Systems.- Bose-Einstein Condensation.- Coherence and Superfluidity of Gaseous Bose-Einstein Condensates.- Ultracold Atoms and Bose-Einstein Condensates in Optical Lattices.- Canonical Statistics of Occupation Numbers for Ideal and Weakly Interacting Bose-Einstein Condensates.- New Regimes in Cold Gases via Laser-Induced Long-Range I §04§nteractions.- Nonlinear Dynamics.- Dynamics and Self-consistent Chaos in a Mean Field Hamiltonian Model.- Kinetic Theory for Plasmas and Wave-Particle Hamiltonian Dynamics.- Emergence of Fractal Clusters in Sequential Adsorption Processes.- The Hamiltonian Mean Field Model: From Dynamics to Statistical Mechanics and Back.
