Spec and Proj
Richard Thomas.
Algebraic geometry has too many prerequisites. Books often take hundreds of pages before reaching a single example of an algebraic variety. Things can be done in infinite layers of generality (this is the number theorists' fault).
There are two quicker ways in: (1) complex manifolds (not so good for number theorists), or (2) Spec and Proj.
The latter describe the most important algebraic varieties (and schemes) via a
single ring. What could be simpler?
There are some
notes
from previous years.