For a counterpoint, read Shafarevich's "Basic notions of algebra". (Beware: author's meaning of "basic" may differ from own.) It's a book that explains all tho

For a counterpoint, read Shafarevich's "Basic notions of algebra". (Beware: author's meaning of "basic" may differ from own.) It's a book that explains all those abstract algebra concepts by introducing motivating examples for each one of them. It's the next best thing to finding the natural setting for them yourself.