The solutions for all long operators of the N=4 SYM theory at one loop
and  of its dual, the classical superstring theory
on AdS5xS5 space, will be presented in terms of their algebraic curves 
encoding all conservation laws. The SYM theory is treated by the Bethe 
ansatz equations in the thermodynamical limit, whereas the 
classical superstring is solved by the finite gap method, using the 
integrability. In a  special (Frolov-Tseytlin)  limit both curves 
coincide, demonstrating the full AdS/CFT correspondence among 
states/operators, including fermions.