I strongly suggest avoiding this book until the authors produce a more readable/useable next edition. Or else just go find an alternative book. The subject matter is quite interesting and useful but the book makes it extremely difficult to learn. For the sake of definiteness I will provide a technical example without defining terminology: There is a figure 3.5 on page 41 which shows a planar graph and its abstraction into a "PQ-tree", containing P-nodes and Q-nodes. P-nodes are cut vertices in Bk and Q-nodes are 2-connected components of Gk. Bk is shown in the figure, as is the PQ-tree. Gk is not shown but aside from the virtual vertices it ought to correspond to Bk. The problem is that Bk clearly has two cut vertices whereas only one cut vertex is represented in the PQ-tree as a P-node. So there is obviously a missing piece of information: How does a Bk cut vertex get translated into a Q-node 2-connected component of Gk? It is at best incomplete and confusing, at worst just wrong. This is not the exception: it is the rule for how the book is written. Only by re-re-re-reading sections and filling in omitted details does one arrive at what the authors should have said. This is not clever. This is not "economical writing". This is wasting the reader's time making the subject unnecessarily difficult. If I were to peer-review chapters 1 through 3 of this book for a journal article I would recommend Do Not Publish Without Major Revisions. I appreciate that the authors started to write this book; they just need to finish it, please.