Main branches of mathematics

The Mathematical Atlas might be useful. Quote from the front page:

Welcome! This is a collection of short articles designed to provide an introduction to the areas of modern mathematics and pointers to further information, as well as answers to some common (or not!) questions. The material is arranged in a hierarchy of disciplines, each with its own index page ("blue pages").

EDIT: It seems that the website no longer available. However, you can still browse it through the internet archive: link.

A somewhat flawed but possibly useful classification can be found at here. This is the American Mathematical Society's mathematics subject classification.

Source: EPRS, where it is available an A-Z list of all research areas within the EPSRC portfolio and all research areas within this theme.