Written primarily for graduate students and researchers, this book introduces two of the main directions of one-dimensional dynamics. The first is a theory of combinational dynamics; it is based on the Sharkovski theorem. The second measures complexity and "chaos" by studying the topological entropy of a system. The book aims to provide a unified and detailed exposition of these developments for internal and circle maps. Chapters cover preliminaries, interval maps, circle maps, and entropy. Appendixes discuss graph maps and rotation theory. Alseda and Llibre teach at the Universitat Aut=noma de Barcelona. Misiurewicz teaches at Indiana University and Purdue University. Annotation c. Book News, Inc., Portland, OR (booknews.com)