This is a great tool for those who want to learn Sanskrit but lack a very thorough understanding of linguistics. Many Sanskrit textbooks have been criticized for presupposing a certain level of linguistic sophistication, which was usually developed through Latin and Greek courses, before attempting to tackle Sanskrit. Egenes realized that many people interested in learning Sanskrit were English speakers with no background in synthetic languages. So what he has created with his "Introduction to Sanskrit," as he mentions in the introductory chapter, is a sort of pre-primer, in so much as this book is an introduction to an introduction. After going through Part 1 (Part 2 of his series focuses mostly on reading practice and prosody, I believe), you will be ready to move on to a more traditional, dense textbook, like Goldman's "Devavanipravesika," Coulson's "Teach Yourself Sanskrit," Desphande's "SamskrtaSubodhini," etc.
"Introduction to Sanskrit" is not, though, a piece of fluff which will teach you very little, in a mind-numbingly slow fashion. By the end of the book you will have learned: the devanagari syllabary, the seven cases and how to decline many types of nouns, a healthy number of verb tenses, how to recognize how to make sandhi changes, and built up a good-sized vocabulary. And as someone who was an absolute neophyte when they came to this book, the challenge is daunting! Sandhi, if not handled gradually like Egenes did, could be enough to drive many people away from Sanskrit. But thankfully, Egenes approached all of the difficult aspects of Sanskrit with sympathy for the learner (especially the autodidact, which many budding Sanskritists are these days); he paced the book so that it would challenging enough to hold our interest, but without alienating us with pedantry. It was very rewarding to know that after completing this book that I could comprehend, with the aid of a dictionary, sections of the "Bhagavad Gita."
So with that I will conclude my rambling with simply this: Egene's "Introduction to Sanskrit" is a godsend to the student of Sanskrit, and I'd encourage anyone interested in learning the language to study with it before moving on to any other text.