Variance gamma is a pure jump stochastic process that allows to control volatility, skewness and kurtosis. The good fit to market data of option prices modeled with variance gamma has attracted increasing interest in the process, seen as an ideal candidate to improve classic Black and Scholes's option pricing. This monograph provides an excellent overview of the research to date on option pricing under variance gamma. The book will be invaluable to practitioners and academics who want to easily implement the model and understand the theory behind it. The monograph offers in-depth explanation of the pricing problem and provides a detailed implementation of finite difference algorithms used to price options. As the only published work that offers ready-to-use algorithms for a wide array of European and American, vanilla and barrier options, it is a great resource for researchers that want to use variance gamma to improve their risk management, trading and theoretical research. The monograph also presents programming code in C implementing every numerical algorithm presented in the work, making the research immediately usable even to the non-expert reader.