This review discusses the theory of inflation and reheating in cosmology, focusing on the dynamics of adiabatic and entropy/isocurvature perturbations, which are key to testing inflationary models. It covers the theory and phenomenology of reheating and preheating after inflation, providing a unified discussion of both gravitational and non-gravitational features of multi-field inflation. The paper also explores inflation in theories with extra dimensions and alternative models like the curvaton scenario and modulated reheating for generating large-scale density perturbations. It discusses observational implications of adiabatic-isocurvature correlations and non-Gaussianity. Inflation is introduced as a solution to cosmological problems such as the flatness and horizon problems, and it generates density perturbations that seed large-scale structure in the universe. The inflationary paradigm predicts nearly scale-invariant spectra of density perturbations, which have been confirmed by observations of the Cosmic Microwave Background (CMB). The paper reviews the dynamics of inflation, including the conditions for slow-roll inflation, the number of e-foldings required to solve cosmological puzzles, and various inflationary models such as large-field, small-field, hybrid, and double inflation. The paper also discusses cosmological perturbations, including scalar, vector, and tensor modes, and their evolution during inflation. Scalar perturbations are related to the curvature perturbation, while vector perturbations are associated with anisotropic stress, and tensor perturbations correspond to gravitational waves. The paper reviews the field equations for scalar perturbations, the evolution of metric perturbations during preheating, and the role of the curvaton and modulated reheating scenarios in generating density perturbations. It concludes with a discussion of the observational implications of inflationary models and future directions in the field.This review discusses the theory of inflation and reheating in cosmology, focusing on the dynamics of adiabatic and entropy/isocurvature perturbations, which are key to testing inflationary models. It covers the theory and phenomenology of reheating and preheating after inflation, providing a unified discussion of both gravitational and non-gravitational features of multi-field inflation. The paper also explores inflation in theories with extra dimensions and alternative models like the curvaton scenario and modulated reheating for generating large-scale density perturbations. It discusses observational implications of adiabatic-isocurvature correlations and non-Gaussianity. Inflation is introduced as a solution to cosmological problems such as the flatness and horizon problems, and it generates density perturbations that seed large-scale structure in the universe. The inflationary paradigm predicts nearly scale-invariant spectra of density perturbations, which have been confirmed by observations of the Cosmic Microwave Background (CMB). The paper reviews the dynamics of inflation, including the conditions for slow-roll inflation, the number of e-foldings required to solve cosmological puzzles, and various inflationary models such as large-field, small-field, hybrid, and double inflation. The paper also discusses cosmological perturbations, including scalar, vector, and tensor modes, and their evolution during inflation. Scalar perturbations are related to the curvature perturbation, while vector perturbations are associated with anisotropic stress, and tensor perturbations correspond to gravitational waves. The paper reviews the field equations for scalar perturbations, the evolution of metric perturbations during preheating, and the role of the curvaton and modulated reheating scenarios in generating density perturbations. It concludes with a discussion of the observational implications of inflationary models and future directions in the field.