This course focuses on the description of mechanisms and physical processes responsible for the emission observed from populations of Galactic and extra-galactic sources in the high-energy portion of the electromagnetic spectrum (mostly X-ray and Gamma-ray). All the phenomena will be illustrated using results from state-of-the-art X-ray and Gamma ray observatories. Students will be able to critically comprehend and discuss the high-energy emission properties of different classes of cosmic sources (e.g. compact X-ray sources such as X-ray binaries and Active Galactic Nuclei, clusters of galaxies, exploding stars such as Supernovae and Gamma Ray Burst, the Galactic Center). Through a multi-wavelength (and multi-messenger) approach, students will be able relate the X-ray properties of the observed sources with their emission at other wavelengths (and other messengers). The student is expected also to attain a basic knowledge of the techniques related to the detection of X-ray and Gamma-ray photons and on the properties of past, present, and future X-ray telescopes.