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I am struggling with that book which I find to be more of second-guessing type than a book for self-study: it has cryptically written sections, no examples (and those given, and rarely, are even more cryptic than the text they are supposed to illustrate), with chapter VIII being a good example of abysmal indigestion...

Good introductions are found in the online series: Socratica's and Macauley's. The Harvard online series uses another book...

My question: Do you know of any online series on abstract algebra that uses MacLane's Algebra?

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    $\begingroup$ I know books Birkhoff & MacLane (1941) and MacLane & Birkhoff (1967). Is there another Algebra just by MacLane? $\endgroup$ Jun 4, 2019 at 12:13
  • $\begingroup$ For searches, it seem important to include a space: "Mac Lane". $\endgroup$ Jun 4, 2019 at 12:31
  • $\begingroup$ @GeraldEdgar Neither MathSciNet nor the University of Michigan Library knows of another "Algebra" book by Mac Lane without Birkhoff. On the other hand, the OP's description, "cryptically written" etc., certainly doesn't fit my memory of Birkhoff & Mac Lane, one of the first books from which I learned (what was then called) modern algebra $\endgroup$ Jun 4, 2019 at 17:30
  • $\begingroup$ Note the related, but not duplicated post. $\endgroup$
    – amWhy
    Jun 4, 2019 at 19:35
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    $\begingroup$ For self-study of undergraduate/beginning graduate it seems Dummit and Foote's 3rd edition is a healthy goal. If you actually finish it then you've done well. Of course there are dozens of other great books; Nicholson, Beachy and Blair, Gallian for starters, I like Hungerford's undergrad. book also. Get old editions and read everything. $\endgroup$ Jun 5, 2019 at 2:23

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