This book contains lectures given by leading scientists from internationally reputed centers of research and teaching who provide insight into the state of the art of scientific computing in relativity. It is split into four parts covering numerics, computer algebra, visualization, and exotic smoothness on spacetime. As well as introducing the techniques the authors stress the importance of combining complementary methods to attack complex problems in general relativity and gravitation. Care has been taken to select lecturers who teach in a comprehensible way, so this work provides an excellent introduction to scientific computing for students who wish to specialize in relativity, gravitation, and/or astrophysics.

Color Plates.- I: Numerics.- 1. Numerical Relativity and Black-Hole Collisions.- 2. Four Lectures on Numerical Relativity.- 3. Alternatives to Finite Difference Methods in Numerical Relativity.- 4. Temporal and Spatial Foliations of Spacetimes.- 5. Rotating and Oscillating Neutron Stars.- 6. Rotating Boson Stars.- 7. Numerical Investigation of Cosmological Singularities.- II: Computer Algebra.- 8. Overview of Computer Algebra in Relativity.- 9. Two-Loop Quantum Gravity with the Computer Algebra Program FORM.- 10. The Mathematic Packages CARTAN and MathTensor for Tensor Analysis.- 11. A Quadratic Curvature Lagrangian of Paw?owski and Raczka: A Finger Exercise with MathTensor.- 12. The Program CRACK for Solving PDEs in General Relativity.- 13. Algebraic Programming in the Hamiltonian Version of General Relativity.- 14. Causal Structure and Integrability in Moving Frames with Reduce.- III: Visualization.- 15. Four Lectures on Computer Graphics and Dkta Visualization.- 16. Visualization in Curved Spacetimes. I. Visualization of Objects via Four-Dimensional Ray-Tracing.- 17. Visualization in Curved Spacetimes. II. Visualization of Surfaces via Embedding.- IV: Exotica.- 18. Exotic Smoothness on Spacetime.- List of Figures.- List of Tables.