General state-space Markov chain theory has evolved to make it both more accessible and more powerful. Markov Chain Monte Carlo in Practice introduces MCMC methods and their applications while also providing some theoretical background. Considering the broad audience, the editors emphasize practice rather than theory and keep the technical content to a minimum. They offer step-by-step instructions for using the methods presented and show the importance of MCMC in real applications with examples ranging from the simple to the more complex in fields such as archaeology, astronomy, biostatistics, genetics, epidemiology, and image analysis.
Almost 2 decades later this book is still a great resource for delving deeper into MCMC. (It may explain the basics well too, but since I already knew those, I can't judge their exposition from a newbie's perspective.)
The chapters on reparameterization, model determination, and model checking have been invaluable to my recent work and are very clearly written; I look forward to the other chapters too.