Self-Study Regimen

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What are the prerequisites to self study projective geometry and universal algebra? The farthest I've gotten is undergraduate abstract algebra: Groups, Rings, Fields. Of course there is a lot left, but specifically what books should I read? I still have no experience in analysis, was considering Rudins book. For the algebra I was going to read Dummit and Foote. After I read these will I be ready for universal algebra and projective geometry?