This is a fairly unambigious question but it hasn't been asked before so I thought I would ask it myself:
Which old books do the modern masters recommend?
There are old books where the mathematical fields explored there have been so thoroughly plowed by later mathematicians that it would be extremely naive and foolish to think that anything of value can still be salvaged from them. Those books are no longer read for the purposes of inspiring research in that area, but are curiosities which are mainly consulted for historical purposes. These are not the old books I am talking about.
The type of old book I refer to is one which still has treasures hidden inside it waiting to be explored. Such is for example Gauss's Disquisitiones Arithmeticae, which Manjul Bhargava claimed inspired his work on higher composition laws, for which he won the 2014 Fields medal.
This is why we need the opinion of the modern masters in the field as to which books are worth consulting today, because only a master in any given field (with his experience of the literature etc) can point us to the fruitful works in that field.
If you list a book, please include the quote of the master who recommended it.
Here is my attempt at the first two:
Fields medallist Alan Baker recommends Gauss's Disquisitiones Arithmeticae in his book A Comprehensive Course of Number Theory: "The theory of numbers has a long and distinguished history, and indeed the concepts and problems relating to the field have been instrumental in the foundation of a large part of mathematics. It is very much to be hoped that our exposition will serve to stimulate the reader to delve into the rich literature associated with the subject and thereby to discover some of the deep and beautiful theories that have been created as a result of numerous researches over the centuries. By way of introduction, there is a short account of the Disquisitiones Arithmeticae of Gauss, and, to begin with, the reader can scarcely do better than to consult this famous work."
Andre Weil recommends Euler's Introductio in Analysin Infinitorum for today's Precalculus students, as quoted by J D Blanton in the preface to his translation of that book: "... our students of mathematics would profit much more from a study of Euler's Introductio in analysin infinitorum, rather than of the available modern textbooks."
I feel this question will be found useful by many people who are looking to follow Abel's advice in a sensible and efficient manner, and I hope this question is clear-cut enough that it doesn't get voted for closure.
Edit: Thanks to Bye-World for bringing up the question of who qualifies as an old master. My response is that any great dead mathematician should qualify as an old master, so Grothendieck is an old master for instance.
