This lecture notes provide a comprehensive review of holographic renormalization, a method used to renormalize quantum field theories (QFTs) on the boundary of asymptotically anti-de Sitter (AdS) spacetimes. The notes begin by discussing mathematical results on asymptotically AdS spacetimes and then outline the general method of holographic renormalization. The method is illustrated through a detailed example: a massive scalar field on AdS spacetime. Key topics include the derivation of the on-shell renormalized action, holographic Ward identities, anomalies, RG equations, and the computation of renormalized one-, two-, and four-point functions. The notes also discuss the application of the method to holographic RG flows and show that the results of the near-boundary analysis of asymptotically AdS spacetimes can be analytically continued to apply to asymptotically de Sitter (dS) spacetimes. Specifically, the Brown-York stress-energy tensor of dS spacetime is shown to be equal to the corresponding tensor of an associated AdS spacetime, up to a dimension-dependent sign.This lecture notes provide a comprehensive review of holographic renormalization, a method used to renormalize quantum field theories (QFTs) on the boundary of asymptotically anti-de Sitter (AdS) spacetimes. The notes begin by discussing mathematical results on asymptotically AdS spacetimes and then outline the general method of holographic renormalization. The method is illustrated through a detailed example: a massive scalar field on AdS spacetime. Key topics include the derivation of the on-shell renormalized action, holographic Ward identities, anomalies, RG equations, and the computation of renormalized one-, two-, and four-point functions. The notes also discuss the application of the method to holographic RG flows and show that the results of the near-boundary analysis of asymptotically AdS spacetimes can be analytically continued to apply to asymptotically de Sitter (dS) spacetimes. Specifically, the Brown-York stress-energy tensor of dS spacetime is shown to be equal to the corresponding tensor of an associated AdS spacetime, up to a dimension-dependent sign.