Seeking the Recommendation on Complexity Theory books

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S.E advisers,

I am a rising college junior in US with a major in mathematics and an aspiring applied mathematician in the fields of theoretical computing. I just recently got a research project on the complexity theory about the algebraic computation, approximation, and measure theory. I am curious if there is both introductory and comprehensive books on the complexity theory with specific focus on my area. Could you guide me?

Sincerely,

PK

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The professor who assigned the project should be happy to provide appropriate references.

I do not know about your particular fieds, but for general complexity theory the classic is Papadimitriou and the modern is Arora-Barak.