This relates to an earlier question you asked:

What representative examples of modules should I keep in mind?

My answer is the same: look at the frontispieces of Miles Ried's book undergrad commutative algebra, which visualize this central fact: Modules to rings are what bundles are to varieties.

This relates to an earlier question you asked:

What representative examples of modules should I keep in mind?

My answer is the same: look at the frontispieces of Miles Ried's book undergrad commutative algebra, which visualize this central fact: Modules to rings are what bundles are to varieties.