Since its inception in the early decades of the twentieth century, quantum mechanics has joined Einstein's theory of relativity and Darwin's theory of evolution as a dominating scientific force. Nevertheless, this theory has steadfastly resisted interpretation within a conventional world view. There is no consensus among workers in the field as to how to solve these problems. In the past, books dealing with these issues have been constrained by two complementary difficulties. At the instructional level, the theoretical apparatus of quantum theory is complex and unfamiliar; textbooks are therefore forced to concentrate heavily on the technical aspects of the theory. At the popular level, considerable attention is often devoted to these questions; but owing to their non-technical nature, such presentations are necessarily limited in the understanding they can convey. The Quantum Challenge is explicitly intended to fill the gap between these two approaches. The authors believe that the material can be presented with reasonable rigor and intellectual honesty, yet still be accessible to undergraduate physical science, mathematics and engineering students.