We are now closer than ever to the fundamental goal of physics of understanding all physical phenomena as the inevitable consequences of few simple principles. The grand unified theory of the strong, weak and electromagnetic interactions has, among other things, explained the quantization of charge, determined the magnitude of the neutral current, and had dramatic impact on cosmology. This book is designed to bring interested students and researchers rapidly up to the point where they can contribute to this exciting field. A substantial text provides a review of the subject. In particular, several chapters are devoted to cosmology and the theory of galaxy formation. A selection of original papers is reprinted. A brief review of group theory is also provided. It is a must for all students and researchers in the field.

The conceptofspontaneous symmetry breaking plays a fundamental role in contemporary physics. It is essential for the description of degenerate ground states, massless modes, and topological defects. Examples are abundant in condensed matter physics, atomic and particle physics, as well as in astro physics and cosmology. In fact, spontaneous symmetry breaking can be re garded as a cornerstone ofa whole branch ofphysics which intersects the above mentioned traditionally distinct fields. In the year 2000 the European Science Foundation (ESF) started the Pro gramme "Cosmology in the Laboratory" (COSLAB), with the goal to search for and to develop analogies betweencondensed matterphysics, particle physics, and cosmology. Not surprisingly, spontaneous symmetry breaking is among the most useful notions in that endeavour. It has been decided that in the sec ond year of the Programme a School should be held in order to work out and deliver to a wide audience of students synthetic overviews of achievements and of current research topics of COSLAB. This idea has been supported by the Scientific and Environmental Affairs Division of NATO by including the School in the renowned series of its Advanced Study Institutes. The School, entitled" Patterns of Symmetry Breaking", was held in Cracow during 16-28 September 2002. It gathered 17 lecturers and about 60 students. The present volume contains notes ofmost of the lectures from that School. We hope that of the physics of spon it will convey to the reader the breadth and the beauty taneous symmetry breaking.

This book provides comprehensive coverage of the current state-of-the-art in soft magnetic materials and related applications, with particular focus on amorphous and nanocrystalline magnetic wires and ribbons and sensor applications. Expert chapters cover preparation, processing, tuning of magnetic properties, modeling, and applications. Cost-effective soft magnetic materials are required in a range of industrial sectors, such as magnetic sensors and actuators, microelectronics, cell phones, security, automobiles, medicine, health monitoring, aerospace, informatics, and electrical engineering. This book presents both fundamentals and applications to enable academic and industry researchers to pursue further developments of these key materials. This highly interdisciplinary volume represents essential reading for researchers in materials science, magnetism, electrodynamics, and modeling who are interested in working with soft magnets.

Frustrated spin systems have been first investigated five decades ago. Well-known examples include the Ising model on the antiferromagnetic triangular lattice studied by G H Wannier in 1950 and the Heisenberg helical structure discovered independently by A Yoshimori, J Villainn and T A Kaplan in 1959. However, extensive investigations on frustrated spin systems have really started with the concept of frustration introduced at the same time by G Toulouse and by J Villain in 1977 in the context of spin glasses. The frustration is generated by the competition of different kinds of interaction and/or by the lattice geometry. As a result, in the ground state all bonds are not fully satisfied. In frustrated Ising spin systems, a number of spins behave as free spins. In frustrated vector spin systems, the ground-state configuration is usually non-collinear. The ground state of frustrated spin systems is therefore highly degenerate and new induced symmetries give rise to unexpected behaviors at finite temperatures. Many properties of frustrated systems are still not well understood at present. Theoretically, recent studies shown in this book reveal that established theories, numerical simulations as well as experimental techniques have encountered many difficulties in dealing with frustrated systems. In some sense, frustrated systems provide an excellent testing ground for approximations and theories. Experimentally, more and more frustrated materials are discovered with interesting properties for applications.