Michio Suzuki (19261998) was one of the 20th century pioneers of modern Group Theory. When I found his books Group Theory I and Group Theory II my first thought was that I had to wait a while before any books of him become accessible to me. I was pleasantly surprised that, unlike say Lang, his writings about Group Theory are written to explain Group Theory to the uninitiated, instead of documenting Group Theory for the experts. At least, that's my expression. So these are my preferred books on Group Theory for now.
Links:
 In memoriam M. Suzuki
 Suzuki, Group Theory I
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