A wonderful book which overviews a lot of these kinds of ideas is Glimpses of Algebra and Geometry by Gabor Toth. From the product description, "The purpose of Glimpses of Algebra and Geometry is to fill a gap between undergraduate and graduate mathematics studies. It is one of the few undergraduate texts to explore the subtle and sometimes puzzling connections between number theory, classical geometry and modern algebra in a clear and easily understandable style."
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