How to Read Michael Artin's Algebra

Question

I am currently reading Algebra by Michael Artin (for self study). I'm finding the book pretty interesting, but I'm still not sure how I should study the book. For example, should I try to prove every theorem as I read the book or should I just read the proof for the theorems? Also, when I take notes, I usually just write down all the theorems, proposition, lemmas, etc. Is this a good way to take notes? And one last question: how should I deal with seemingly impossible exercises? I have experiences with proofs from Olympiad math, and from learning Calculus (rigorously), but there seem to be some exercises that takes a very long time to figure out.