I used this when writing my Master's Thesis on Transcendental Number Theory. The book is very thorough; it starts with proofs of the irrationality of root 2, then Liouville's result about transcendence (and his example). It then moves into proving the irrationality of both e and pi, using the classical results of Lambert, and then it uses the historical extensions to prove the Hermite-Lindemann-Weirstrass results that pi and e are transcendental. It goes on to discuss the works of Siegal, Mahler, and Baker, all important contributors to transcendental number theory.
Transcendental Number Theory is an area that has long been one almost impossible to approach for an undergraduate. There was a paucity of literature, and most of it devoted to (i) graduate students, or (ii) specialists in the field. Lang can elegantly prove the transcendence of e using complex analysis in about a page. Most undergraduates don't have the background or sophistication to read such proofs, nor to digest the monographs.
This book fills that niche. It is targeted to undergraduates. To that end they make you work for the results, and there are several gaps in the proofs that are left as "challenges". It is great for developing mathematical maturity, but some of them can be quite hard and frustrating. Additional references on topics like symmetric equations, continued fractions, or complex analysis can help you through some of those stumbling blocks. There are no exercises.
If you're an accomplished graduate student this book isn't targeted to you. It feels hand-holdie. Other books would be Mahler's lectures on Transcendental Number Theory or Gelfond's book on Transcendental and Algebraic Numbers that are more succinct. If you want an encyclopedic reference those books are better. Making Transcendence Transparent is ill suited as such a reference because of its tone, wordiness, and those gaps.
Finally, as the other reviewer noted, the bibliography is very small. There is much more literature out there than this, and the book gives few clues for future reading.
Despite that, this book fills the targeted niche precisely. At the very least, a curious undergraduate can get a healthy respect for the magnitude of work required to prove some of the classical results, and such an exposition is not normally attempted (or severely succinct) in most other books that are out there. While it's not a research monograph, it's not trying to be.