I am searching for a good book (or survey paper) on treewidth. I would be delighted if the book/paper surveys multiple approaches to treewidth (eg: structural, algorithmic, `language-theoretic') and also discusses on treewidth in isolation.
The book I found is Treewidth: Computations and Approximations, by Ton Kloks. This book approaches treewidth from a structural point of view (partial $k$-tree, chordal completion) and also algorithmic point of view. It covers treewidth computation and approximation in special graph classes, and talks about treewidth bounded graphs.
Is this book a must-read? Or is there any other choice out there?
I liked the game theoretic definition of treewidth in the survey Practical algorithms for MSO model-checking on tree-decomposable graphs, Langer et. al. It is equivalent to the traditional tree-decomposition based definition in a natural way (As a sidenote, now there is a game theoretic approach to MSO model checking).
Could you point out a book/paper on treewidth that keeps multiple appraches to it in mind?