This lecture introduces synchrotron and X-ray free electron laser (XFEL) radiation, highlighting their significance in various scientific fields. It discusses the intense beams of X-rays produced by these facilities and their applications in advanced manufacturing, biological imaging, nanotechnology, and more. The instructor outlines the fundamental principles of X-ray interaction with matter and the physics behind generating synchrotron and XFEL radiation. The lecture also covers the experimental methods and applications utilized at these facilities, emphasizing three main methodologies: elastic scattering and diffraction, X-ray spectroscopies, and X-ray imaging. Each methodology is explored in detail, starting with crystallography and elastic scattering techniques, followed by spectroscopic methods that can only be performed at synchrotrons. The final section focuses on imaging techniques, including X-ray tomographies and lensless imaging. The instructor invites students to engage with the diverse and evolving world of synchrotron and XFEL science, which spans numerous scientific disciplines.