I am so glad to hear about people wanting to learn about special relativity, general relativity, the thermodynamics of the earth, Euler's equations, basically everything! I want to respond to a lot of this stuff (and I will do my best) before getting to my personal favourite...
I like the bizarre theory of Time Dilation and the Twin Paradox.
I particularly loved learning that the Twin Paradox is probably not a real paradox (non-uniform motion breaks the symmetry). The concept that light is an immutable 'thing' (and not time) was groundbreaking and has plenty of applications.
[-b +or- (b^2-4ac)^.5]/2a
I think that I got it right.
Yeah, you got it right.
Herndon Georeactor theory
I hope we never discover this to be true.
It might not be true but it is somewhat close - radioactive decay might keep the mantle molten, although probably not fission or fusion.
Phi, the most awesomest ratio ever.
Phi owns.
Anyways, my favourite theorems (so far) are Cauchy's integral theorem and Cauchy's residue theorem - really the same thing, but anyways - They're super useful, they reduce the complexity of difficult problems, and give us an interesting way to find series and integrals.
(Close second: Heisenberg uncertainty principle. It is a useful and interesting quantum mechanical measurement tool, a Fourier pair relation, and an explanation of various quantum mechanical oddities.)
Sniped:
I still don't know what a Lorentz transform is
There are Galilean transformations, which allow us to change between coordinate systems - even between coordinate systems that are moving relative to one another - in our day to day life (IE: The coordinate grid centred around your house can be transformed into the coordinate grid centred around your car via Galilean transformations). Lorentz transforms are an extension or modification to Galilean transformations so that light has a constant velocity in every coordinate frame, which is an assumption of Special relativity. (It does a lot more than that, but I'll save that for your physics prof to teach you)