What kind of maths do I need to know for general relativity and where can I learn about it ?

Question

please recommend me any maths book where I can learn what I need for general relativity.

Answer 1

you need to know some differential geometry, and for that you need to understand calculus of several variables very well.

http://www.hofstra.edu/~matscw/diff_geom/tc.html

you can also try these books:
Exploring Black Holes: Introduction to General Relativity,
by Edwin F. Taylor, John Archibald Wheeler
Spacetime and Geometry: An Introduction to General Relativity by Sean Carroll
A First Course in General Relativity by Bernard F. Schutz
Gravity: An Introduction to Einstein's General Relativity by James B. Hartle

Answer 2

I would recommend Michael Spivak's "Calculus on Manifolds". It is a small (maybe 100 pages) book and can be read independently. The only prerequisite is mulitvariable calculus and "mathematical sophistication", although some acquantaince with matrix algebra would be helpful.

That said, this is only the tip of the iceberg. But from here you can attempt to tackle more serious books on differential geometry. For instance, you can look at Spivak's five volumes on differential geometry.

Answer 3

You need to be comfortable with calculus and linear algebra to a very serious level.

Hmm, books... "Qantum Field Theory" by Michael Peskin. "Gravitation" - big black book, I forget who wrote it. I say, go to a bookstore, take a look at the books and determine what math is missing from your education.