This article discusses the theory of cosmological perturbations, focusing on the generation of primordial fluctuations and the role of inflation in addressing fundamental cosmological problems. It begins by characterizing perturbations in a homogeneous universe, describing how metric and matter perturbations can be represented mathematically. The article then explores gauge transformations and the issue of fictitious perturbations, highlighting the importance of gauge-invariant variables to avoid misleading interpretations. Key variables like the gravitational potential Φ and the canonical quantization variable ν are introduced, along with their roles in describing perturbations. The article explains how inflation solves the homogeneity, flatness, and inhomogeneity problems of the early universe. It outlines the conditions under which inflation occurs, emphasizing the need for accelerated expansion to ensure a flat and homogeneous universe. The generation of primordial fluctuations is discussed, focusing on quantum fluctuations during inflation and their evolution. The article describes how these fluctuations are stretched to cosmic scales and how they result in the observed cosmic microwave background (CMB) temperature fluctuations. The robustness of inflationary predictions is examined, including the nearly scale-invariant spectrum of perturbations, the spectral index $n_s$, and the Gaussian nature of perturbations. The article also considers alternative scenarios, such as non-flat spectra and non-adiabatic perturbations, and their associated challenges. It concludes by emphasizing the significance of inflation in explaining the large-scale structure of the universe and the observed CMB anisotropies.This article discusses the theory of cosmological perturbations, focusing on the generation of primordial fluctuations and the role of inflation in addressing fundamental cosmological problems. It begins by characterizing perturbations in a homogeneous universe, describing how metric and matter perturbations can be represented mathematically. The article then explores gauge transformations and the issue of fictitious perturbations, highlighting the importance of gauge-invariant variables to avoid misleading interpretations. Key variables like the gravitational potential Φ and the canonical quantization variable ν are introduced, along with their roles in describing perturbations. The article explains how inflation solves the homogeneity, flatness, and inhomogeneity problems of the early universe. It outlines the conditions under which inflation occurs, emphasizing the need for accelerated expansion to ensure a flat and homogeneous universe. The generation of primordial fluctuations is discussed, focusing on quantum fluctuations during inflation and their evolution. The article describes how these fluctuations are stretched to cosmic scales and how they result in the observed cosmic microwave background (CMB) temperature fluctuations. The robustness of inflationary predictions is examined, including the nearly scale-invariant spectrum of perturbations, the spectral index $n_s$, and the Gaussian nature of perturbations. The article also considers alternative scenarios, such as non-flat spectra and non-adiabatic perturbations, and their associated challenges. It concludes by emphasizing the significance of inflation in explaining the large-scale structure of the universe and the observed CMB anisotropies.