This document presents a course on gravitation, covering Newtonian and Einsteinian theories, delivered at the African Institute for Mathematical Sciences (AIMS) in Cameroon in 2018 and 2019. The course aims to provide a comprehensive overview of gravitation, showing how Einstein's theory of relativity naturally extends Newton's. It is structured into three main parts: Newton's physics, Einstein's theory of relativity, and the general-relativistic world. The first chapter reviews Newtonian mechanics and gravitation, while the second introduces special and general relativity, and the third explores relativistic manifestations such as gravitational waves and black holes. The course includes exercises to encourage active learning. The author acknowledges the support of colleagues and students, and references influential works in the field. The content is based on a combination of established texts and personal insights, with a focus on both theoretical and practical aspects of gravitation. The course emphasizes the transformation of coordinates, the role of the metric tensor, and the use of variational principles in mechanics. It also discusses the implications of relativity for space-time, the behavior of objects in non-inertial frames, and the conservation laws in physics. The material is designed to provide a solid foundation for understanding the evolution of gravitational theories from Newton to Einstein.This document presents a course on gravitation, covering Newtonian and Einsteinian theories, delivered at the African Institute for Mathematical Sciences (AIMS) in Cameroon in 2018 and 2019. The course aims to provide a comprehensive overview of gravitation, showing how Einstein's theory of relativity naturally extends Newton's. It is structured into three main parts: Newton's physics, Einstein's theory of relativity, and the general-relativistic world. The first chapter reviews Newtonian mechanics and gravitation, while the second introduces special and general relativity, and the third explores relativistic manifestations such as gravitational waves and black holes. The course includes exercises to encourage active learning. The author acknowledges the support of colleagues and students, and references influential works in the field. The content is based on a combination of established texts and personal insights, with a focus on both theoretical and practical aspects of gravitation. The course emphasizes the transformation of coordinates, the role of the metric tensor, and the use of variational principles in mechanics. It also discusses the implications of relativity for space-time, the behavior of objects in non-inertial frames, and the conservation laws in physics. The material is designed to provide a solid foundation for understanding the evolution of gravitational theories from Newton to Einstein.