Notes on Hawking radiation Alessio Miscioscia Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany E-mail: alessio.miscioscia@desy.de Abstract: In these notes we explore the basics of Hawking radiation in black holes’ physics. First we review the original Hawking derivation and we then present a modern derivation, closer to the usual intuition, and also the rigorous deirvation from aximatic approches to quantum field theories (in curved background). Notes prepared for the Desy theory Workshop (13.06.2023) and Desy theory workshop (09.01.2024).