Here is a nice note about Dedekind-Hasse norm for quadratic number fields.
Here are notes about Weierstrass Division Theorem and its consequences (proving that power series rings over fields are UFD).
Here is an introduction to category theory.
Here are nice notes on Dedekind domains.
Here are some interesting examples of projective modules.
Here is the foundational paper by Richard Swan establishing relation between vector bundles and projective modules.