Over the past 20-30 years, kt theory has rekindled its historic ties with biology, chemistry, and physics as a means of creating more sophisticated descriptions of the entanglements and properties of natural phemena - from strings to organic compounds to DNA. This volume is based on the 2008 AMS Short Course, Applications of Kt Theory. The aim of the Short Course and this volume, while t covering all aspects of applied kt theory, is to provide the reader with a mathematical appetizer, in order to stimulate the mathematical appetite for further study of this exciting field. No prior kwledge of topology, biology, chemistry, or physics is assumed. In particular, the first three chapters of this volume introduce the reader to kt theory (by Colin Adams), topological chirality and molecular symmetry (by Erica Flapan), and DNA topology (by Dorothy Buck). The second half of this volume is focused on three particular applications of kt theory. Louis Kauffman discusses applications of kt theory to physics, Nadrian Seeman discusses how topology is used in DNA natechlogy, and Jonathan Simon discusses the statistical and energetic properties of kts and their relation to molecular biology.