This review discusses particle-theory models of inflation and their predictions for the primordial density perturbation, which is believed to be the origin of structure in the universe. It covers mini-reviews of observational cosmology, elementary field theory, and supersymmetry, and focuses on the spectral index \( n(k) \), which will be a powerful discriminator between models when measured with high accuracy by Planck. The review also treats new models firmly rooted in modern particle theory and incorporating supersymmetry. It is addressed to both astrophysicists and particle physicists, with each section designed to be self-contained regarding background knowledge. The review begins by introducing the concept of inflation, explaining how it sets the initial conditions for the hot big bang and addresses issues such as the absence of unwanted relics and the initial density parameter. It then delves into the slow-roll paradigm, detailing the evolution of the inflaton field and the predictions for the spectrum and spectral index of the curvature perturbation. The review also discusses the calculation of the curvature perturbation generated by inflation, including single-component and multi-component inflatons, and the role of gravitational waves. The section on field theory and the potential covers renormalizable and non-renormalizable theories, lagrangians, internal symmetries, and the true vacuum. It also explores supersymmetry, quantum corrections to the potential, and non-perturbative effects. The review then examines various forms of the potential, including monomial and exponential potentials, and the implications for the spectral index. The discussion of supersymmetry includes its motivation, algebra, lagrangians, spontaneous symmetry breaking, soft SUSY breaking, and loop corrections. The review also covers hybrid inflation, where the inflaton field is less than the Planck scale, and the role of F-terms and D-terms in determining the potential. Finally, the review concludes with a discussion of the observational constraints on inflation models, emphasizing the importance of the spectral index \( n(k) \) and the potential for detecting gravitational waves. The review aims to provide a comprehensive overview of the current status of inflation model building, focusing on particle theory and supersymmetry.This review discusses particle-theory models of inflation and their predictions for the primordial density perturbation, which is believed to be the origin of structure in the universe. It covers mini-reviews of observational cosmology, elementary field theory, and supersymmetry, and focuses on the spectral index \( n(k) \), which will be a powerful discriminator between models when measured with high accuracy by Planck. The review also treats new models firmly rooted in modern particle theory and incorporating supersymmetry. It is addressed to both astrophysicists and particle physicists, with each section designed to be self-contained regarding background knowledge. The review begins by introducing the concept of inflation, explaining how it sets the initial conditions for the hot big bang and addresses issues such as the absence of unwanted relics and the initial density parameter. It then delves into the slow-roll paradigm, detailing the evolution of the inflaton field and the predictions for the spectrum and spectral index of the curvature perturbation. The review also discusses the calculation of the curvature perturbation generated by inflation, including single-component and multi-component inflatons, and the role of gravitational waves. The section on field theory and the potential covers renormalizable and non-renormalizable theories, lagrangians, internal symmetries, and the true vacuum. It also explores supersymmetry, quantum corrections to the potential, and non-perturbative effects. The review then examines various forms of the potential, including monomial and exponential potentials, and the implications for the spectral index. The discussion of supersymmetry includes its motivation, algebra, lagrangians, spontaneous symmetry breaking, soft SUSY breaking, and loop corrections. The review also covers hybrid inflation, where the inflaton field is less than the Planck scale, and the role of F-terms and D-terms in determining the potential. Finally, the review concludes with a discussion of the observational constraints on inflation models, emphasizing the importance of the spectral index \( n(k) \) and the potential for detecting gravitational waves. The review aims to provide a comprehensive overview of the current status of inflation model building, focusing on particle theory and supersymmetry.