Walter Harding Maurer, a lecturer in Sanskrit at Pennsylvania State University, prepared a textbook of India's classical language for his own courses in the early 1990s, and ultimately Routledge published it for all to use in the mid-1990s. Routledge originally published it in two handsome hardback volumes, but as this was printed in very limited quantities and used copies go for hundreds of dollars, it is probable that any student wishing to purchase this textbook will turn to Routledge's later paperback reprinting.
And that's a damn shame, because the budget-priced reprinting is one of the poorest-quality paperbacks I have ever seen, especially from a respectable academic publisher. Routledge have combined the two hardback volumes into a single 850-page paperback. It's ungainly, and it has a cheap glue binding. The spine will start to crack when you're still in the initial chapters, and pages will be falling out liberally when you're only halfway through the book. If you come across a copy of the hardback version at anything approaching a reasonable price, grab it while you can.
I would recommend that total beginners (by which I mean neophytes to Sanskrit who already have a solid grounding in Greek and Latin) turn to Hart's A Rapid Sanskrit Method (ISBN 8120801997), which is marvelously friendly and effective. Maurer's is more of an intermediate textbook as the sheer amount of vocabulary he presents in each chapter is likely to daunt readers looking for a mere introduction. However, Maurer's book does have great value in its exercises (translations into Sanskrit really help to reinforce what one has learned), its fine clarification of Sanskrit idiom, and its enjoyable reading passages.
Coming to Sanskrit as a complete beginner, and having worked through the first 15-20 chapters so far in a course, I have found this to be quite a good text for the novice. Though Maurer's approach is I think unnecessarily philological at times, it's there if you're interested and the writing is generally lively. Also, he rapidly moves from the rudiments into native structures and idioms, which is great, even if I sometimes think there's too much vocabulary to absorb so quickly. The readings are interesting and incidentally introduce many cultural concepts and give you a good feel for Indian life and Hindu thought (hard as it is to generalize about those). Overall, I think if you are willing to work at it the book does a wonderful job of guiding you from square 1 to reading your first minimally adapted or unadapted Sanskrit texts, and provides some enjoyment along the way.