  In this dissertation we explore various aspects of the AdS/CFT
correspondence. As string quantization on general backgrounds with fluxes is
very difficult, one often uses the duality at the level of canonical fields of
supergravity and the corresponding half-BPS operators in SYM, since they both
belong to the shortest multiplets of the superconformal group SU(2,2|4). In
addition to half-BPS operators, there are others with non-renormalization
properties. One such class of operators is the quarter-BPS operators, which are
dual to threshold bound states of elementary supergravity excitations. Their
scaling dimension is also determined by their internal quantum numbers.
Extended superspace methods make it simple to identify and remove descendant
pieces from quarter-BPS candidates. We also compute three-point functions
involving quarter-BPS operators, and explain how their non-renormalization
translates into statements about the dual supergravity quantities. But we can
go beyond discussing protected operators. The GS superstring on AdS(5) x S(5)
can be quantized exactly in the limit where the AdS(5) radius R goes to
infinity and the R-charge J scales like R^2. BMN states are then dual to single
trace operators with certain phases inserted (BMN operators). BMN operators are
another natural generalization of half-BPS operators. The perturbative
expansion of scaling dimensions of BMN operators is in powers of gN/J^2.
Moreover, one can do perturbation theory around the infinite R, J ~ R^2 limit.
Both expansions have the same regime of validity in string theory and in SYM.
We calculate the first 1/R^2 and 1/J corrections, and find complete agreement
between the dual quantities.
