What areas of maths play the main role in the theory of general relativity?

Tim C: What areas of maths play the main role in the theory of general relativity?
I know general relativity is highly mathematical and requires very advanced mathematics. I am just curious, can you please point out what areas of maths is used in general relativity? Just giving me the names will be fine…eg. differential equations. Thanks!

Answers and Views:

Answer by Emma C
Integrals, Calculas, Linear Algebra
Tensors (they don’t come up many other places), Guages

Answer by Cisco
Tensor calculus and differential geometry.