A new edition of Meyn & Tweedie – what for?
The majority of topics covered in this book are well established. Ancient topics such as the Doeblin decomposition and even more modern concepts such as f-regularity are mature and not likely to see much improvement. Why then is there a need for a new edition?
Publication of this book in the Cambridge Mathematical Library is a way to honor my friend and colleague Richard Tweedie. The memorial article  contains a survey of his contributions to applied probability and statistics and an announcement of the initiation of the Tweedie New Researcher Award Fund. Royalties from the book will go to Catherine Tweedie and help to support the memorial fund.
Richard would be very pleased to know that our book will be placed on the shelves next to classics in the mathematical literature such as Hardy, Littlewood, and Pólya's Inequalities and Zygmund's Trigonometric Series, as well as more modern classics such as Katznelson's An Introduction to Harmonic Analysis and Rogers and Williams' Diffusions, Markov Processes and Martingales.
Other reasons for this new edition are less personal.
Motivation for topics in the book has grown along with growth in computer power since the book was last printed in March of 1996. The need for more efficient simulation algorithms for complex Markovian models, or algorithms for computation of optimal policies for controlled Markov models, has opened new directions for research on Markov chains [29, 113, 10, 245, 27, 267]. It has been exciting to see new applications to diverse topics including optimization, statistics, and economics.