As a humble ESL teacher, not a linguist, this was my first experience of a linguistics approach to grammar. I would highly recommend it to anyone who is somewhat familiar with standard grammar textbooks and would like to pursue a deeper, more exploratory approach to the subject.
At first I was surprised by some of the terminology until I switched into the critical and descriptive mindset. This book starts to look at the logic of language which underlies the so-called grammar rules found in textbooks. In a way, it actually simplifies one's understanding of grammar (in a positive sense) because, rather than an endless list of apparently arbitrary rules and exceptions for different situations, it provides an outline description of why those rules are the way they are.
I don't think it would be possible to use this material directly in teaching, because it requires the fine sensibility of an educated native speaker to appreciate some of the nuances, and the technical language of linguistics-based grammar theory is different to that of the textbook grammar theory with which ESL students are familiar. However, the critical approach is extremely useful for ESL teachers because it can help us clarify our own understanding of the language points we are trying to teach. Understanding the language structures at a deeper level than that at which we are teaching them can only be helpful. It makes the clarification stage of grammar teaching more natural and effortless.
The book is written in a beautifully functional but relaxed style. It provides a critical and intelligent overview of English grammar categories from the perspective of two cutting-edge linguists. Geoffrey Pullum, by the way, is known elsewhere for his highly amusing and cynical essays on the world of linguistics and publishing. Apart from its superlative content, A Student's Introduction to English Grammar is also a testament to the stylistic versatility of the authors.