The paper discusses the string spectrum in flat space and pp-waves from the large $N$ limit of $\mathcal{N} = 4$ Super Yang Mills. The authors reproduce the spectrum by summing a subset of planar Feynman diagrams and provide a heuristic argument for neglecting other diagrams. They also explore other aspects of pp-waves, including a matrix model associated with the DLCQ description of maximally supersymmetric eleven-dimensional pp-waves. The introduction explains the connection between large $N$ gauge theories and string theory, highlighting the AdS/CFT correspondence for $\mathcal{N} = 4$ Super Yang Mills. The paper then delves into the details of pp-waves as limits of $AdS_p \times S^q$ geometries and the spectrum of strings on pp-waves. It discusses the simplification of the action in light cone gauge and the identification of the string spectrum with operators in the Yang-Mills theory. The authors derive the string spectrum from the gauge theory perspective, focusing on states with large R charge and finite $\Delta - J$. They show that the spectrum of single trace operators in the Yang-Mills theory corresponds to the spectrum of string modes on pp-waves. The paper concludes with a discussion on the matrix model for the DLCQ description of M-theory plane waves, including the Hamiltonian formulation and the interpretation of solutions.The paper discusses the string spectrum in flat space and pp-waves from the large $N$ limit of $\mathcal{N} = 4$ Super Yang Mills. The authors reproduce the spectrum by summing a subset of planar Feynman diagrams and provide a heuristic argument for neglecting other diagrams. They also explore other aspects of pp-waves, including a matrix model associated with the DLCQ description of maximally supersymmetric eleven-dimensional pp-waves. The introduction explains the connection between large $N$ gauge theories and string theory, highlighting the AdS/CFT correspondence for $\mathcal{N} = 4$ Super Yang Mills. The paper then delves into the details of pp-waves as limits of $AdS_p \times S^q$ geometries and the spectrum of strings on pp-waves. It discusses the simplification of the action in light cone gauge and the identification of the string spectrum with operators in the Yang-Mills theory. The authors derive the string spectrum from the gauge theory perspective, focusing on states with large R charge and finite $\Delta - J$. They show that the spectrum of single trace operators in the Yang-Mills theory corresponds to the spectrum of string modes on pp-waves. The paper concludes with a discussion on the matrix model for the DLCQ description of M-theory plane waves, including the Hamiltonian formulation and the interpretation of solutions.