Help studying the derived functor of the limit functor

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I am currently working through the second half of Hatcher's algebraic topology and through Weibel's Homological algbera. In the latter the next chapter I am going to read is the derived functor of the limit functor. And in the former section 3.F discusses this as well.

I was wondering if any of you had any suggestion to best read these two different sources to get the most out of each. To be clear, I will be anyway reading both, but want to make this as efficient and fruitful as possible.

Any tips or even opinions are accepted.