I have been trying to relearn parts of algebra (mostly module theory and (advanced)linear algebra) from Lang, which, frankly, is not going too well.
Now, I have managed to get my hands on 'Aluffi - Algebra: Chapter 0'. And it (specifically the section called linear algebra reprise) seems pretty good. But, before I jump in and start studying from it, I want to make sure that I won't be repeating my experience with Lang. One indicator could be that it is a popular textbook. But, on searching, I found that it is not much used elsewhere.
Has anyone taken a formal/reading course using this book or studied it at length (not just leafed through it) and can thus recommend it and if it's possible (and not asking too much of their time) could they write briefly the course plan they followed?
Added This is in response to KCd's comments
What I am trying to do before next semester, is to take stock and make notes on some topics in Algebra generally taught in the first year of grad school (I am not in grad school. Will apply for Fall 2013). The notes will be (or on topics from) basic module theory, tensors, some exterior algebra, basic commutative algebra (an example of a topic would be Localization) (Some of these things I have learnt in courses such as Differential Geometry, etc.)
For instance, in the note which will end with a proof of the structure theorem over PIDs (hopefully one that I am truly comfortable with), I began with defining free modules via universal property, instead of how I had learned it from Artin's book.
Earlier, I thought I'll do this while relearning from Lang. But that's not serving me too well, for reasons I am not entirely clear about. Then I came upon Aluffi's book.
[@KCd: Let me also add that when I was trying to write up a note on basic Galois Theory, I came across your expository notes. They are spectacular.]