Linear Algebra - A basic knowledge of linear algebra is essential to the study of differential geometry. The linearisation of a smooth map features heavily throughout differential geometry as do determinants, traces, eigenvalues and eigenvectors. Many of the fundamental objects studied in differential geometry are tensor fields which incorporate and extend undergraduate linear algebra.

Topology - A basic knowledge of topology is very useful in the study of differential geometry - it provides a language and structure for notions relating to continuity and allows us to generalise from Euclidean submanifolds to manifolds as objects in their own right. Our focus is in what is often called point set topology. We won't be so interested in algebraic topology, and in particular we won't spend much time discussing coffee cups and donuts.

Differential Calculus - Differential calculus is essential to the study of differential geometry - that's the differential part!

Integral Calculus - Integral calculus is essential to the study of differential geometry - it's the counterpoint to differential calculus and is as important in differential geometry as it is in calculus.