Fundamental Examples

Here is another nice crowd-sourced resource from MathOverflow.net:  a list of fundamental examples in mathematics.

http://mathoverflow.net/questions/4994/fundamental-examples

From the premise that a single example can often shape an entire mathematical discipline, a list of such examples is generated.

The list includes examples like the harmonic series in Real and Complex Analysis; the Brachistochrone problem in Physics; the Gaussian integers in Algebra; the Platonic solids in Geometry; and the Seven Bridges of Konigsberg in Graph Theory.

This is a great resource that provides accessible entry points to a lot of advanced mathematics!