Though most people seem to advise against reading Mac Lane's "Categories for the working mathematician", and neither did I read it from start to finish, looking at it, I find that it is highly worth trying to read some parts because it's extremely very well written: to the best of my knowledge this book is second to none in his field (of course, nowadays you have also Borceux's book, but its scope is something different). So if your mathematical interests force you to use categories, you'll have to consult Mac Lane's again and again. Starting to read it directly is a way to get an idea of where to find things when you need them.
Ok, there is a problem because, for instance, it begins with "metacategories" (chapter I, section 1), so when you arrive to real categories (section 2) you may be already completely lost. Hence, I asked myself: what parts of Mac Lane did I really have used in my own work and find them useful, worth reading or consulting, or are unavoidable in the language of categories? The following is my own selection of some chapters and sections of Mac Lane's book, based only on my personal tastes and biases (the selection is from the first edition, but, if I'm not wrong, the only difference is that the second one has an extra chapter on monoidal and braided categories and functors near the end):
Chapter I: 2, 3, 4, 5, 8.
Chapter II: 2, 3.
Chapter III: 1, 2, 3, 4, 5
Chapter IV: 1, 2, 4.
Chapter V: 1, 4, 5.
Chapter VI: 1, 2.
Chapter VII: 1, 3, 4, 5, 6.
Chapter VIII: 1, 2, 3, 4.
Chapter IX: 1, 2.
In general, I've tried to avoid both too abstract issues, logical foundations and too specific or specialized matters.
This kind of reading, of course, raises the problem of encountering terms you haven't seen defined before, or results you haven't studied. But in this cases, I think there's no harm in going to the index and find where the term is defined, or taking the result you haven't seen before on faith. Trying to do some exercises is of course necessary and the historical notes at the end of the chapters are interesting too.
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