...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly great generality is in essence the same as a small and concrete special case.
This quote is similar to one of Hilbert:
The art of doing mathematics consists in finding that special case which contains all the germs of generality.
I want to know: What are some good examples of special cases containing all generality?
One answer per post. Community wiki?
In some sense, the theory for the classification of finite-dimensional complex simple Lie algebras and their linear representations is to a large extend given by understanding the theory for the special case of the Lie algebra $\mathfrak{sl}_2(\Bbb C)$.