This volume is dedicated to Jack Hale to mark his 60th birthday on 3 October 1988. It contains invited articles contributed by his friends and colleagues, and in particular by the invited speakers at the symposium on "New Directions in Dynamical Systems'' held in Jack's honour in August 1988 at Brown University. The variety and interest of these articles reflects both the enormous influence that Jack has had on the study of differential equations and dynamical systems, and the esteem and affection in which he is held. All the articles were refereed and have appeared in recent issues of Proceedings Л of the Royal Society of Edinburgh.