Here I will list only books tending to survey large portion of mathematics areas at least at the graduate level, written by competent research mathematicians.

Do not list

No Schaum-cheat and for-dummies editions allowed here. We also do not list dictionaries and encyclopaedias at this moment. The idea is to list books which try to give some connection between various ideas, at the level of ideas, proofs and so on, rather than collections of independently written items or entries (see however the exceptional Princeton companion).

We do not list very valuable series of Handbooks in various areas (algebra vollumes edited by Hazewinkel etc.), nor the long series of books by Serge Lang, which in their entirety belong to the area. We do not list Bourbaki either (mainly because “Elements” are unfinished, hence even more incomplete than planned), but there will be once an entry about him in the main lab. We do not list ancient books (see however ever fresh Felix Klein’s lectures).

List

Felix Klein, Lectures on development of mathematics in 19th century, this book is not only about the history, but also surveys many very deep ideas, central in the mathematics of 19th century, especially in algebraic geometry, number theory and analysis. The exposition is still fresh, mathematically interesting and not an easy reading.