Math books emphasizing geometrical aspects (for differential geometry).

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I'm not very good at geometry, but I feel, most of the time, math concepts in calculus, linear algebra, complex analysis, abstract algebra etc. can only be intuitively understood when and if an appeal to geometry is made. Therefore, I'm looking for book recommendations to bridge this gap.

I'm looking for books:

  1. That treat the usual subjects (algebra, complex analysis, analytic geometry, topology), etc., with a geometrical flavor, making analytic/algebraic rules and results plausible.

  2. Introduce geometry itself and may help develop intuition and feel for the subject so I can tackle differential geometry later on.

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