“General Relativity and Beyond. A compact course”, curated by Salvatore Capozziello, is an advanced course intricately designed for graduate students, researchers, and professionals in the realms of Cosmology, Astrophysics and Theoretical High Energy Physics. This curriculum not only navigates through the core principles of general relativity but significantly emphasizes the revolutionary studies of gravitational waves, alongside delving into extended theories of gravity and non-metric theories, to unravel the mysteries of the cosmos. The course is meticulously organized into three comprehensive segments: Foundations of General Relativity, Gravitational Waves, and Beyond General Relativity, providing a robust framework that spans from Einstein's foundational theories to the cutting-edge research in gravitational physics. The journey begins with a solid foundation in the principles of general relativity, where students revisit Einstein's Field Equations and explore their profound implications on the understanding of spacetime, black holes, and the overall structure of the universe. This foundational knowledge sets the stage for the groundbreaking segment dedicated to Gravitational Waves. In the Gravitational Waves segment, the course delves deeply into the theoretical predictions, discovery, and study of gravitational waves, marking a new era in astrophysics. Students will explore how these ripples in the fabric of spacetime, caused by cataclysmic events such as the merging of black holes or neutron stars, provide a novel means of probing the universe. The course covers the detection techniques, instruments like LIGO and Virgo, and the significant discoveries that have transformed our understanding of the universe, emphasizing the role of gravitational waves in testing the predictions of general relativity and alternative theories of gravity. Advancing further, the course explores Extended Theories of Gravity and Non-Metric Theories, where students engage with the theoretical and mathematical extensions of Einstein's theory. This includes scalar-tensor theories, f(R) theories, each offering insights into addressing cosmological puzzles such as dark matter, dark energy, and the early universe's inflation. The course also investigates non-metric theories that challenge traditional spacetime concepts, pushing the boundaries of our understanding of gravity. By the conclusion of this course, participants will have gained a comprehensive understanding of gravitational waves' pivotal role in astronomy and astrophysics, a thorough grounding in general relativity, and an insightful exploration into the extended and non-metric theories of gravity. They will be equipped to critically assess these theories, apply them to cosmic phenomena, and contribute to the forefront of gravitational research. Recommended readings include "Beyond Einstein Gravity" by S. Capozziello and V. Faraoni, which provides an extensive overview of alternative gravitational theories, and "Noether Symmetries in Theories of Gravity" by F. Bajardi and S. Capozziello, offering insights into the conservation laws and symmetries within these theories. These resources, alongside other seminal texts and recent research articles, will enable students to explore the forefront of gravitational