There are four books which I'm pretty sure I'll never be without...
Geometry: A Comprehensive Course by Dan Pedoe
An Introduction to Differential Geometry by T. J. Willmore
Riemannian Geometry by Manfredo P. do Carmo
Topics in Algebra by I. N. Herstein
When I lost my original collection of math books, these were the first books I set out to re-acquire (except Topics in Algebra
, which I had with me when I lost the rest) because they cover the aspects of mathematics I find most important.
While I know most of what is covered in them (specially An Introduction to Differential Geometry
and Riemannian Geometry
), I always feel better having them within reach. And in the cases of Geometry
and Topics in Algebra
, they hold a lot of knowledge I'd really like to have a better mastery of than I currently possess.