Since the 1970s, set theory has developed in several directions. The most outstanding results cover the application of sophisticated techniques to problems in analysis, topology, infinitary combinatorics and other areas of mathematics. This book contains a selection of contributions, some of which are expository in nature, embracing various aspects of the latest developments in the late 1990s. Amongst topics treated are forcing axioms and their applications, combinatorial principles used to construct models, and a variety of other set theoretical tools including inner models, partitions and trees. This book should be of interest to graduate students and researchers in foundational problems of mathematics.