I am certainly interested (I have, heaven help us!, a master's degree in mathematic), and I can be of help here - but I'm a lousy teacher.

Assuming that we want to look at *interesting* mathematics (rather than just currently *useful* mathematics), then the classes of numbers are great fun - counting numbers, integers, rational, real, algebraic, transcendental, complex, etc. And, no, there is not just one sentence to be said about each of them.