In this introductory review we discuss dynamical tests of the AdS_5 x S^5 string/N=4 super Yang-Mills duality. After a brief introduction to AdS/CFT we argue that semiclassical string energies yield information on the quantum spectrum of the string in the

degeneratedstringcon guration.

πt=κτρ=0γ=

˙ t=√

=

=√√2π˙=coshρt222π√2˙1 φ

˙2 φ˙1=sinγcosψφ√J:=J1+J2.2π˙2=0,sin2γsin2ψφ

HenceclassicallyE=J.Onemaynowconsiderquantum uctuationsaroundthisµsolution,i.e.Xµ=Xsolution(τ)+1

λ

E=√√

λheld xed.Thislimitofalargequantum

numbersuppressesallthehigherloopcontributionsbeyondone-loop,i.e.

E J=E2(κ)+1 J→∞E4(κ)+... →E2(κ).J(9)

Hencethequadraticapproximationbecomesexact!Thisquadratic uctuationac-tion(includingthefermions)isnothingbuttheIIBsuperstringinaplanewavebackground

[6],whicharisesfromtheAdS5×S5geometrythroughaso-calledPen-roselimit(see[29,30]forthisconstruction).Thequantizationofthisstringmodel