It is a new edition of the book with the same title that was issued in (1984; Zbl 0559.58012). Since the first edition appeared, great progress has been made in the field, and the updated publication has been essentially revised and complemented. However the general structure is the same: the book contains a small introduction by the editor which is devoted to the description of the main aspects in the chaos phenomenon (part 1), a reprint of the original articles treating different problems of the chaos phenomenon subdivided into ten sections (part 2), and an extensive bibliography (part 3). The introduction has been rewritten and contains many new conceptions and techniques in the field (e.g., applied symbolic dynamics, characterization of chaotic attractors, etc.) The main part has been essentially changed and although the new edition contains only 37 titles as compared to 41 in the first edition (there are 24 new articles added, while 28 articles from the older edition have been omitted), the book is far more voluminous. The bibliography has been extended up to 67 books and more than 2200 articles and limited basically by the first half of 1989.