Ergodic theory is a field that is lively on its own and also in its interactions with other branches of mathematics and science. In recent years the interchanges with harmonic analysis have been especially noticeable and productive in both directions. The 1993 Alexandria Conference explored many of these connections as they were developing. The three survey papers in this book describe the relationships of almost everywhere convergence (J. Rosenblatt and M. Wierdl), rigidity theory (R. Spatzier), and the theory of joinings (J.-P. Thouvenot). These papers present the background of each area of interaction, the most outstanding recent results, and the currently promising lines of research. They should form perfect starting points for anyone beginning research in one of these areas. The book also includes thirteen research papers that describe recent work related to the theme of the conference: several treat questions arising from the Furstenberg multiple recurrence theory, while the remainder discuss almost everywhere convergence and a variety of other topics in dynamics.

The author presents the fundamentals of the ergodic theory of point transformations and several advanced topics of intense research. The study of dynamical systems forms a vast and rapidly developing field even when considering only activity whose methods derive mainly from measure theory and functional analysis. Each of the basic aspects of ergodic theory--examples, convergence theorems, recurrence properties, and entropy--receives a basic and a specialized treatment. The author's accessible style and the profusion of exercises, references, summaries, and historical remarks make this a useful book for graduate students or self study.