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I have the following advice for reading papers: read them (up to) three times.

The first time through, you do not check that the claims are correct. You are attempting to get broad structural understanding. Don't even look at the proofs. Many details will be left dangling. This is fine. This is your first pass. If you are doing a lot of reading, leave a note to yourself that you have read this paper coarsely.

If there is something in the paper justifying further understanding, read it again. This time, read through the proofs quickly. Again, don't check any details. Just ask yourself: "Is this the sort of argument I have seen before? Does this structure of proof match the broad structure I got from my first reading?" If you are doing a lot of reading, or might come back to this paper in the future, leave a note to yourself that you have read this paper.

If there is still something in the paper to justify detailed understanding, read it a third time. Check every line. Ask yourself "why should I believe this is true" as often as possible. If a particular claim needs an additional idea (for you to believe it), record this idea in the margin nearby. If you are doing a lot of reading, or might come back to this paper in the future, leave a note to yourself that you have read this paper in detail.

You leave notes to yourself because you trust yourself to have applied the appropriate level of skepticism to the things you have read.

There are not enough hours in the day to read everything at the detailed level. For results that are entirely predictable, you should arrive at that conclusion after one or maybe two readings (and you will have recorded that you believe those results at that level). Only the results with complexity or surprise should merit a third read.

Is this method perfect? No. Does it help allocate time better? I think so.

How does this apply to textbooks? You can certainly write in your textbooks, so leaving notes should be no problem. Clearly, the "big theorems" should be read three (or more) times. Other results may only need to be believed at the "plausible" (coarse, once read) or "likely" (medium, twice read) level. Is this ideal? Probably not, but neither of us is immortal, so some accommodation of finite time must occur.