Green-Schwarz string in AdS(5)xS(5): semiclassical partition function

A systematic approach to the study of semiclassical fluctuations of strings in AdS(5) x S-5 based on the Green-Schwarz formalism is developed. We show that the string partition function is well defined and finite. Issues rela ted to different gauge choices are clarified. We consider explicitly severa l cases of classical string solutions with the world surface ending on a li ne, on a circle or on two lines on the boundary of AdS. The first example i s a BPS object and the partition function is one. In the third example the determinants we derive should give the first corrections to the Wilson loop expectation value in the strong coupling expansion of the N = 4 SYM theory at large N.