I read the first two chapters of Algorithm Design by Jon Kleinberg and Éva Tardos. The prose is very clear and lucid, but it has one problem: it's incredibly long-winded. A good editor could probably lop off a good 1/4 of the book without loss of info. That would make the book spectacular.

Also, if anyone is interested, these lecture notes [0] (Algorithmic Math by Soicher & Vivaldi) below introduces algos from elementary number theory/abstract algebra.

[0] http://www.maths.qmul.ac.uk/~lsoicher/ambook.pdf