In 1964 the author's mono graph "Differential- und Integral-Un- gleichungen," with the subtitle "und ihre Anwendung bei Absch?tzungs- und Eindeutigkeitsproblemen" was published. The present volume grew out of the response to the demand for an English translation of this book. In the meantime the literature on differential and integral in- equalities increased greatly. We have tried to incorporate new results as far as possible. As a matter of fact,...