This Teubner-Text contains selected contributions to the "10th Conference on Problems and Methods in Mathematical Physics (10th TMP)", held at the Technical University of Chemnitz-Zwickau in Chemnitz, Germany, September 13 - 17, 1993. The main topics of the conference were Scientific Computing in Solid and Fluid Mechanics Problems with Singularities Boundary Integral Methods Multilevel Finite Element Methods Free Boundary Value Problems and Optimal Control Numerical Functional Analysis. The conference brought together more than 170 experts from 17 countries, and the 18 plenary and invited lectures as well as the 120 short lectures were devo- ted to plenty of problems and latest results in applied mathematical research. Undoubtedly, the majority of these contributions would have deserved publi- cation. However, this volume does not intend to reflect the whole scientific contents of the conference in the usual form of proceedings. It is rather aiming at giving a survey of some recent trends in fields covered by the topics of this meeting. The organizing committee hopes that this Teubner-Text reflects the main spirit of the 10th TMP.