I had read/studied most of this book when I was a graduate student in chemical engineering at Syracuse University (in 1987-88). I also took two courses on the subject from Professor Troutman. I strongly recommend this book to any "newcomer" to the subject. The author is a mathematician, and a large fraction of the book consists of theorems, lemmas, propositions, corollaries (and their rigorous proofs). The book also contains, however, a good number of illustrative examples and exercises which make it useful to engineers and scientists as well as to students of mathematics who want to learn more about applications of mathematics to physical sciences.