Title: A must own book but very challenging....
Product review: I was introduced to this book when I first took a course on Perturbation and Asymptotic Methods. The chapters on Boundary Layer theory, and WKB theory are well written and fun to read. In addition, I also found Summation of Series chapter quite interesting in regards to accelerated convergence (a numerical technique that is sadly ignored in beginning numerical methods courses). My only gripe with this book is the difficulty of some of the problems. Not all problems are difficult, but as someone else mentioned, even some of the "Intermediate" exercises are quite daunting. Regardless, I think this is a MUST OWN book for any scientist/engineer in a research/teaching field. As a supplement to this book, I also recommend reading Chapter 6 (titled Perturbation Theory) in Landau and Lifshitz Vol. 3 (Quantum Mechanics Non-Relativistic Theory).
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