Astrophysical Black Holes: A Compact Pedagogical Review

Black holes are among the most extreme objects that can be found in the Universe and an ideal laboratory for testing fundamental physics. This article will briefly review the basic properties of black holes as expected from general relativity, the main astronomical observations, and the leading astrophysical techniques to probe the strong gravity region of these objects. It is mainly intended to provide a compact introductory overview on astrophysical black holes to new students entering this research field, as well as to senior researchers working in general relativity and alternative theories of gravity and wishing to quickly learn the state of the art of astronomical observations of black holes.