This book addresses graduate students in the first place and is meant as a modern compendium to the existing texts on black hole astrophysics. The authors present in pedagogically written articles our present knowledge on black holes covering mathematical models including numerical aspects and physics and astronomical observations as well. In addition, in their write-up of a panel discussion the participants of the school address the existence of black holes consenting that it has by now been verified with certainty.

During the first decades after Einstein had developed his Theory of General Relativity, the main effort was to understand the theory and verify it experimentically. Meanwhile Genral Relativity is one of the experimentally best confirmed theories and has become a powerful tool for the investigation of cosmic processes where strong gravitational fields are involved.
This book contains 16 contributions from well-known experts giving a broad overview for non-specialists who want to learn how to purely academic issues like gravitational wave detectors are now put into reality.

In this book we display the fundamental structure underlying classical electro dynamics, i. e., the phenomenological theory of electric and magnetic effects. The book can be used as a textbook for an advanced course in theoretical electrodynamics for physics and mathematics students and, perhaps, for some highly motivated electrical engineering students. We expect from our readers that they know elementary electrodynamics in the conventional (1 + 3)-dimensional form including Maxwell's equations. More over, they should be familiar with linear algebra and elementary analysis, in cluding vector analysis. Some knowledge of differential geometry would help. Our approach rests on the metric-free integral formulation of the conservation laws of electrodynamics in the tradition of F. Kottler (1922), E. Cartan (1923), and D. van Dantzig (1934), and we stress, in particular, the axiomatic point of view. In this manner we are led to an understanding of why the Maxwell equa tions have their specific form. We hope that our book can be seen in the classical tradition of the book by E. J. Post (1962) on the Formal Structure of Electro magnetics and of the chapter "Charge and Magnetic Flux" of the encyclopedia article on classical field theories by C. Truesdell and R. A. Toupin (1960), in cluding R. A. Toupin's Bressanone lectures (1965); for the exact references see the end of the introduction on page 11. ."

For this set of lectures we assumed that the reader has a reasonable back ground in physics and some knowledge of general relativity, the modern theory of gravity in macrophysics, and cosmology. Computer methods are present ed by leading experts in the three main domains: in numerics, in computer algebra, and in visualization. The idea was that each of these subdisciplines is introduced by an extended set of main lectures and that each is conceived as being of comparable 'importance. Therefpre we believe that the book represents a good introduction into scientific I computing for any student who wants to specialize in relativity, gravitation, and/or astrophysics. We took great care to select lecturers who teach in a comprehensible way and who are, at the same time, at the research front of their respective field. In numerics we had the privilege of having a lecturer from the National Center for Supercomputing Applications (NCSA, Champaign, IL, USA) and some from other leading institutions of the world; visualization was taught by a visualization expert from Boeing; and in com puter algebra we took recourse to practitioners of different computer algebra systems as applied to classical general relativity up to quantum gravity and differential geometry.

This book presents a fresh, original exposition of the foundations of classical electrodynamics in the tradition of the so-called metric-free approach. The fundamental structure of classical electrodynamics is described in the form of six axioms: (1) electric charge conservation, (2) existence of the Lorentz force, (3) magnetic flux conservation, (4) localization of electromagnetic energy-momentum, (5) existence of an electromagnetic spacetime relation, and (6) splitting of the electric current into material and external pieces.
The first four axioms require an arbitrary 4-dimensional differentiable manifold. The fifth axiom characterizes spacetime as the environment in which the electromagnetic field propagates a" a research topic of considerable interest a" and in which the metric tensor of spacetime makes its appearance, thus coupling electromagnetism and gravitation. Repeated emphasis is placed on interweaving the mathematical definitions of physical notions and the actual physical measurement procedures.
The tool for formulating the theory is the calculus of exterior differential forms, which is explained in sufficient detail, along with the corresponding computer algebra programs. Prerequisites for the reader include a knowledge of elementary electrodynamics (with Maxwell's equations), linear algebra and elementary vector analysis; some knowledge of differential geometry would help. Foundations of Classical Electrodynamics unfolds systematically at a level suitable for graduate students and researchers in mathematics, physics, and electrical engineering.

Computer Simulation and Computer Algebra. Starting from simple examples in classical mechanics, these introductory lectures proceed to simulations in statistical physics (using FORTRAN) and then explain in detail the use of computer algebra (by means of Reduce). This third edition takes into account the most recent version of Reduce (3.4.1) and updates the description of large-scale simulations to subjects such as the 170000 X 170000 Ising model. Furthermore, an introduction to both vector and parallel computing is given.

REDUCE ist ein Kompaktkurs }ber die Anwendung dieses Computer-Algebra-Systems. REDUCE ist an den deutschen Universt{ten weit verbreitet und dient zum symbolischen Rechnen mit dem Computer, wie es fr}her nur mit Papier und Bleistift unter Zuhilfenahme eines Handbuchs der Mathematik m-glich war. Studenten der Informatik, Mathematik, Physik, Chemie, der Ingenieurwissenschaften u.a. erhalten hier das grundlegende R}stzeug, das ihnen sp{ter auch das Arbeiten mit anderen Computer-Algebra-Systemen erleichtern wird. Auch Wissenschaftlern, die bisher noch nicht symbolisch gerechnet haben, kann dieses Buch uneingeschr{nkt empfohlen werden.