Symbolic Algebraic Methods and Verification Methods The usual implementation” of real numbers as floating point numbers on existing computers has the well known disadvantage that most of the real numbers are not exactly representable in floating point. Also the four basic arithmetic operations can usually not be performed exactly. During the last years research in different areas has been intensified in order to overcome these problems. (LEDA Library by K. Mehlhorn et al. Exact arithmetic with real numbers” by A. Edalat et al. Symbolic algebraic methods verification methods). The latest development is the combination of symbolic algebraic methods and verification methods to so called hybrid methods. This book contains a collection of worked out talks on these subjects given during a Dagstuhl seminar at the Forschungszentrum für Informatik Schloß Dagstuhl Germany presenting the state of the art