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Preface Frequently used notation 1. Approximation by rational numbers 2. Approximation to algebraic numbers 3. The classifications of Mahler and Koksma 4. Mahler's conjecture on S-numbers 5. Hausdorff dimension of exceptional sets 6. Deeper results on the measure of exceptional sets 7. On T-numbers and U-numbers 8. Other classifications of real and complex numbers 9. Approximation in other fields 10. Conjectures and open questions Appendix A. Lemmas on polynomials Appendix B. Geometry of numbers Bibliography Index.