  We review the spectral curve for the classical string in AdS5xS5. Classical
integrability of the AdS5xS5 string implies the existence of a flat connection,
whose monodromies generate an infinite set of conserved charges. The spectral
curve is constructed out of the quasi-momenta, which are eigenvalues of the
monodromy matrix, and each finite-gap classical solution can be characterized
in terms of such a curve. This provides a concise and powerful description of
the classical solution space. In addition, semi-classical quantization of the
string can be performed in terms of the quasi-momenta. We review the general
frame-work of the semi-classical quantization in this context and exemplify it
with the circular string solution which is supported on RxS3 in AdS5xS5.

High Energy Physics - Theory