This paper explores the string spectrum in flat space and pp-waves arising from the large N limit of N=4 Super Yang Mills. The authors show that the spectrum can be reproduced by summing a subset of planar Feynman diagrams and argue that other diagrams can be neglected. They also discuss pp-waves and present a matrix model associated with the DLCQ description of maximally supersymmetric eleven-dimensional pp-waves. The paper begins by introducing the AdS/CFT correspondence and the fact that strings in N=4 Super Yang Mills move in ten dimensions. The radius of curvature of the ten-dimensional space is proportional to (g_YM^2 N)^{1/4}. The spectrum of strings on AdS_5 × S^5 corresponds to the spectrum of single trace operators in the Yang Mills theory. The perturbative string spectrum is not known exactly for general values of the 't Hooft coupling, but is known for large values where the string spectrum in flat space is recovered. The authors then show how pp-waves arise as a limit of AdS × S geometries. They consider the trajectory of a particle moving very fast along the S^5 and focus on the geometry seen by the particle. They perform a coordinate transformation and rescaling to obtain the pp-wave metric. They also discuss the energy and angular momentum along the ψ direction and their scaling in the limit. The paper then discusses strings on pp-waves, showing that they are exactly solvable in both NS and RR backgrounds. The action simplifies in light cone gauge, and the string spectrum is derived from the Yang Mills theory. The authors show that the string spectrum can be reproduced from the gauge theory point of view, and that the spectrum on a pp-wave incorporates the first correction to the flat space result for certain states. The authors also discuss the matrix model associated with the DLCQ compactification of the M-theory plane wave. This matrix model has unusual features such as the absence of flat directions. They show that the matrix model is determined by the supersymmetry algebra of the plane wave metric and that the vacuum energy is zero. The paper concludes by discussing the correspondence between the supergravity modes and the operators in the Yang Mills theory. The authors show that the conformal dimension of the operators matches the string spectrum in the large N limit. They also discuss the mass of the operators and their decay to lower energy states. The paper highlights the importance of the DLCQ description and the matrix model in understanding the string spectrum in flat space and pp-waves.This paper explores the string spectrum in flat space and pp-waves arising from the large N limit of N=4 Super Yang Mills. The authors show that the spectrum can be reproduced by summing a subset of planar Feynman diagrams and argue that other diagrams can be neglected. They also discuss pp-waves and present a matrix model associated with the DLCQ description of maximally supersymmetric eleven-dimensional pp-waves. The paper begins by introducing the AdS/CFT correspondence and the fact that strings in N=4 Super Yang Mills move in ten dimensions. The radius of curvature of the ten-dimensional space is proportional to (g_YM^2 N)^{1/4}. The spectrum of strings on AdS_5 × S^5 corresponds to the spectrum of single trace operators in the Yang Mills theory. The perturbative string spectrum is not known exactly for general values of the 't Hooft coupling, but is known for large values where the string spectrum in flat space is recovered. The authors then show how pp-waves arise as a limit of AdS × S geometries. They consider the trajectory of a particle moving very fast along the S^5 and focus on the geometry seen by the particle. They perform a coordinate transformation and rescaling to obtain the pp-wave metric. They also discuss the energy and angular momentum along the ψ direction and their scaling in the limit. The paper then discusses strings on pp-waves, showing that they are exactly solvable in both NS and RR backgrounds. The action simplifies in light cone gauge, and the string spectrum is derived from the Yang Mills theory. The authors show that the string spectrum can be reproduced from the gauge theory point of view, and that the spectrum on a pp-wave incorporates the first correction to the flat space result for certain states. The authors also discuss the matrix model associated with the DLCQ compactification of the M-theory plane wave. This matrix model has unusual features such as the absence of flat directions. They show that the matrix model is determined by the supersymmetry algebra of the plane wave metric and that the vacuum energy is zero. The paper concludes by discussing the correspondence between the supergravity modes and the operators in the Yang Mills theory. The authors show that the conformal dimension of the operators matches the string spectrum in the large N limit. They also discuss the mass of the operators and their decay to lower energy states. The paper highlights the importance of the DLCQ description and the matrix model in understanding the string spectrum in flat space and pp-waves.