This volume of Lecture Notes In Mathematics contains the proceedings of a research Seminar—Workshop on recent progress In the Analytic Theory of Continued Fractions held at Loen, Norway from June 5 to June 30, 1981. In recent years there has been a renewed Interest in the subject of continued fractions. This Is due In part to the advent of computers and the resulting importance of the algorithmic character of continued fractions. It Is also due to the close connection between continued fractions and Fade approxlmants and their application to theoretical physics. Primary emphasis at the Workshop was on the analytic aspects of the subject; however, considerable attention was also given to applied and computational problems. These interests are reflected In the Workshop proceedings.