This book discusses several models of limit order books and introduces a general, flexible open-source library, useful to readers studying trading strategies in order-driven markets. It begins aby assessing relevant empirical data, moves on to mathematical models, in order to reproduce observed properties, and finally presents a framework for numerical simulations. It covers some of the important modelling techniques in detail, including agent-based modelling, advanced modelling of limit order books based on Hawkes processes, Jaisson and Rosenbaum theories, and LLOB models. The book also provides in-depth coverage of simulation techniques, such as numerical simulation and the limit order book simulator. It will be useful to graduate students in the fields of econophysics, financial mathematics, actuarial mathematics and high frequency financial data.