The book offers contributions to a number of topics in semantics, while at the same time providing an engaging discussion of key foundational issues and of what Property Theory can contribute to them. The book starts from a version of Property Theory which stems out of a combination of the lambda calculus with Aczel's Frege structures (a combination originally developed by Raymond Turner). Fox improves on it and substantially extends it with original applications to plurals and mass nouns, to 'intensional individuals' and to the dynamics of discourse. Some useful appendixes on further extensions and alternatives are added. While being formally highly sophisticated, it manages to give a sense of the elegance and flexibility of the underlying theory. This volume should be of interest to researchers engaged in the cognitive science arena.