This book presents a clear and accessible introduction to the theory of cosmological perturbations. This subject is central to modern cosmology, as scalar cosmological perturbations in the early universe are believed to be the seeds from which today's cosmological structures, such as galaxies and clusters of galaxies, originated. The text begins with an introduction to the fundamentals of Einstein's theory of general relativity and the key elements of the standard cosmological model. The basic ideas of cosmological perturbations and gravitational instability are first developed within a Newtonian framework, providing an intuitive foundation for the fully relativistic treatment presented in later chapters. The final part of the book explores specific models and generalizations of the standard model, including non-adiabatic pressure perturbations, non-standard dark matter and dark energy models, as well as dissipative phenomena. Providing a concise yet wide-ranging treatment of the subject, this book serves as an ideal entry point for graduate students and researchers who wish to build the foundations necessary to explore cosmological perturbation theory in greater depth.