The book is the Proceedings of the Conference ENUMATH 2003, the 5th European Conference on Numerical Mathematics, concerned with most recent achievements in scientific computing, computational mathematics, numerical analysis and their applications. These proceedings contain a selection of invited plenary lectures, papers presented in minisymposia and contributed papers. All contributions to these proceedings have been reviewed by members of the Scientific Committee. Attention is paid to theoretical aspects of new numerical techniques and algorithms, as well as to applications, for example in fluid dynamics, electromagnetic fields, structural mechanics, free boundary problems. The book will be very useful for a wide range of readers, giving them an excellent overview of the most modern methods, techniques, algorithms and results in numerical mathematics, scientific computing and their applications.