This volume reviews the theory and simulation methods of stochastic kinetics by integrating historical and recent perspectives, presents applications, mostly in the context of chemical signal processing, gene expression, enzyme kinetics and autocatalytic processes. In recent years, due to the development in experimental techniques such as optical imaging, single cell analysis, and one-molecule fluorescence spectroscopy, biochemical kinetic data inside single living cells have increasingly become available. The emergence of systems biology brought renaissance in the application of stochastic kinetic methods as is reflected in this book. "This is the first book in a new, highly exciting, growing area of applied mathematics, with applications to modern cell biology. The level is very accessible to a wide range of readers from the physical sciences to biology and the life sciences. ? The book is lucidly written and has an extensive, scholarly researched bibliography which will certainly be useful to anyone who wants to go deeper into the subject." (Hong Qian, SIAM Review, Vol. 57 (3), September, 2015)