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

Fromtheseonededucesincompleteanalogyto(31)thetwocircularstringequations

4λJ12

K(q 1)2

22

π2=J

[(1 q)K(q 1)+qE(q 1)]2,(40)

whichencodetheenergyrelationE=E(J1,J2)uponeliminationofq.Inordertodothisweagainmakeananalyticansatzinλ/J2forqandEaswedidin(32).Thisyieldsthefollowingimplicitexpressionforq0intermsofthe llingfractionJ2/J

J2

K(q 1(41)

0) ,

The rsttwoenergytermsintheλ/J2expansionthentaketheform

E0=1,E1=2