Researchers in spatial statistics and image analysis are familiar with Gaussian Markov Random Fields (GMRFs), and they are traditionally among the few who use them. There are, however, a wide range of applications for this methodology, from structural time-series analysis to the analysis of longitudinal and survival data, spatio-temporal models, graphical models, and semi-parametric statistics. With so many applications and with such widespread use in the field of spatial statistics, it is surprising that there remains no comprehensive reference on the subject. 'Gaussian Markov Random Fields - Theory and Applications' provides such a reference, using a unified framework for representing and understanding GMRFs. Various case studies illustrate the use of GMRFs in complex hierarchical models, in which statistical inference is only possible using Markov Chain Monte Carlo (MCMC) techniques. The preeminent experts in the field, the authors emphasize the computational aspects, construct fast and reliable algorithms for MCMC inference, and provide an online C-library for fast and exact simulation.