Integrability enables us to obtain the complete spectrum of the classical solutions in IIB superstrings on $AdS_5times S^5$ and of the long operators in large N ${cal N}=4$ super Yang-Mills at one-loop. General solutions are described in terms of algebraic curves. I present the construction of the solutions and make a comparison between both sides of AdS/CFT, introducing novel features of supersymmetric Bethe ansatz equations.

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