I asked this question a while back on MO :

One thing that really helped in learning the Serre SS was doing particular computations (like $H^*(CP^{\infty})$)

I am curious, as a sort of followup if anyone can suggest:

- A reference where small computations are carried out? or
- A specific computation to do with a small enough sheaf an some simple topological space that would be able to give one a feel for sheaf cohomology. So this space that we are working over need not be a scheme, in fact it would probably be best if it were not a scheme since I don't understand them quite yet. And are there tricks of the trade to computing these things? or do people just hammer away ate injective resolutions?

In short, please suggest a space and a sheaf on it that I should work on computing the sheaf cohomology of.

**PS:** *I of course welcome any other suggestions for understanding how to compute sheaf cohomology.*