This chapter provides an overview of modern cosmology, focusing on the recent observations of the universe's acceleration, precise measurements of microwave background anisotropies, and the formation of structures like galaxies and galaxy clusters from primordial fluctuations during inflation. The author, Juan Garcia-Bellido, introduces the basic concepts and equations of hot Big Bang cosmology, defining key cosmological parameters and their relationships. He discusses the three fundamental observations that have shaped our current understanding: the universe's acceleration, the distribution of matter on large scales, and the anisotropies in the microwave background. These observations allow for the precise determination of a few cosmological parameters within the inflationary plus cold dark matter paradigm. The chapter also delves into the details of Big Bang cosmology, explaining the expansion of the universe, the relative abundance of light elements, and the cosmic microwave background. It covers the Friedmann-Robertson-Walker (FRW) metric, which describes the universe's geometry, and the equations governing the dynamics of the universe. The author discusses the matter and energy content of the universe, including radiation, matter, and vacuum energy, and how these components contribute to the overall density parameter. The chapter further explores the cosmological parameters such as the Hubble parameter, the age of the universe, the deceleration parameter, and the spatial curvature. It explains how these parameters are used to parametrize the universe's evolution and the various regions and boundaries in the (ΩM, ΩΛ) plane, which specify different behaviors of the universe. The section on the accelerating universe discusses the implications of the universe's expansion rate and the discovery of high-redshift supernovae, which revealed that the universe is accelerating rather than decelerating. This acceleration is attributed to a cosmological constant, a form of dark energy with negative pressure. The chapter also addresses the mystery of the origin and nature of dark energy, noting that its value is many orders of magnitude larger than expected from quantum mechanical zero-point energy. Finally, the chapter reviews the evidence for dark matter, including the flat rotation curves of spiral galaxies, the baryon fraction in galaxy clusters, and weak gravitational lensing. It discusses the large-scale structure formation and the matter power spectrum, highlighting the importance of understanding the nature and amount of matter necessary for structure formation.This chapter provides an overview of modern cosmology, focusing on the recent observations of the universe's acceleration, precise measurements of microwave background anisotropies, and the formation of structures like galaxies and galaxy clusters from primordial fluctuations during inflation. The author, Juan Garcia-Bellido, introduces the basic concepts and equations of hot Big Bang cosmology, defining key cosmological parameters and their relationships. He discusses the three fundamental observations that have shaped our current understanding: the universe's acceleration, the distribution of matter on large scales, and the anisotropies in the microwave background. These observations allow for the precise determination of a few cosmological parameters within the inflationary plus cold dark matter paradigm. The chapter also delves into the details of Big Bang cosmology, explaining the expansion of the universe, the relative abundance of light elements, and the cosmic microwave background. It covers the Friedmann-Robertson-Walker (FRW) metric, which describes the universe's geometry, and the equations governing the dynamics of the universe. The author discusses the matter and energy content of the universe, including radiation, matter, and vacuum energy, and how these components contribute to the overall density parameter. The chapter further explores the cosmological parameters such as the Hubble parameter, the age of the universe, the deceleration parameter, and the spatial curvature. It explains how these parameters are used to parametrize the universe's evolution and the various regions and boundaries in the (ΩM, ΩΛ) plane, which specify different behaviors of the universe. The section on the accelerating universe discusses the implications of the universe's expansion rate and the discovery of high-redshift supernovae, which revealed that the universe is accelerating rather than decelerating. This acceleration is attributed to a cosmological constant, a form of dark energy with negative pressure. The chapter also addresses the mystery of the origin and nature of dark energy, noting that its value is many orders of magnitude larger than expected from quantum mechanical zero-point energy. Finally, the chapter reviews the evidence for dark matter, including the flat rotation curves of spiral galaxies, the baryon fraction in galaxy clusters, and weak gravitational lensing. It discusses the large-scale structure formation and the matter power spectrum, highlighting the importance of understanding the nature and amount of matter necessary for structure formation.