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

totheAdS/CFTproposal,thesetwosetsofparametersaretobeidenti edas

4πλλ=R2

(x y)2 A(λ,1α′,gS)|OA (3)

,gS).with (λ,1

α′

AzerothordertestoftheconjectureisthentheagreementoftheunderlyingsymmetrysupergroupPSU(2,2|4)ofthetwotheories,whichfurnishestherepre-sentationsunderwhichOA(x)and|OA transform.Thisthenyieldsahintonhowonecouldsetupanexplicitstringstate/gaugeoperatordictionary.

Clearlythereislittlehopeofdeterminingeithertheallgenus(allordersingS)stringspectrumorthecomplete1/Ndependenceofthegaugetheoryscalingdimensions .Buttheidenti cationoftheplanargaugetheorywiththefree(gS=0)stringseemsfeasibleandfascinating:FreeAdS5×S5stringtheoryshouldgivetheexactallloopgaugetheoryscalingdimensionsinthelargeNlimit!Unfortunatelythough,ourknowledgeofthestringspectrumincurvedbackgrounds,eveninsuchahighlysymmetriconeasAdS5×S5,remainsscarce.Thereforeuntilveryrecentlyinvestigationsonthestringsideofthecorrespondencewerelimitedtothedomainofthelowenergye ective eldtheorydescriptionofAdS5×S5stringsintermsoftypeIIBsupergravity.This,however,isnecessarilylimitedtoweaklycurvedgeometries√instringunits,i.e.tothedomainof

λ 1.Hence

oneisfacingastrong/weakcouplingduality,inwhichstronglycoupledgauge elds