The LIBOR market model is an interest rate model that is used to price derivatives. Whilst the number of books on interest rate modeling is large, this is a reflection of the speed of development of the theory and market demand. This book will concentrate on two of the most modern models: Heath-Jarrow-Morton and Brace-Gatarek-Musiela. It will concentrate on practical issues: calibration, relations between HJM and BGM models and the accuracy and quality of pricing models. It will will introduce new topics including stochastic volatility, recombining trees for HJM and BGM and factor analysis. This will be backed up by empirical examples and data.