In 1956, a physicist named John Kelly working at Bell Labs published a paper titled A New Interpretation of Information Rate. In the paper he draws an analogy between the outcomes of a gambling game and the transmission of symbols over a communications channel. For a positive expectation game, Kelly showed that a betting system based on a fixed fraction of the bankroll can make the bankroll grow at an exponential rate in the long run. The exponential growth rate in this case is directly analogous to the rate of information transmission through a communications channel. This book examines the Kelly system in detail. Applications of the Kelly system in both gambling and investing are considered. Python code for calculating the Kelly fractions for both a single stock investment and an investment in two stocks simultaneously is included. Included is an introductory review chapter on the probability theory needed to analyze gambling systems in general.There is also a chapter on some of the more commonly used gambling systems such as the Martingale system. This book will be useful for anyone interested in a good mathematical introduction to gambling systems in general, and the Kelly system in particular.