This manuscript presents the lecture notes of a course given during the second training school of COST Action CA18108 "Quantum gravity phenomenology in the multi-messenger approach", which occurred in Belgrade in September 2022. It aims to provide a comprehensive introduction on various aspects of data acquisition and analysis in the context of high-energy gamma-ray astrophysics. A special effort was made so that these lecture notes can be understood by PhD students with no background on instrumentation or gamma-ray astrophysics. So that the lecture is kept short enough, the choice was made to focus on the imaging atmospheric Cherenkov technique.
These lecture notes will walk the reader through the whole analysis process: how raw images are collected and how the raw data are produced, how these raw data are calibrated, how primary particle parameters are reconstructed and how the physical properties of the observed source are extracted. Finally, we will go through the different important points to consider regarding hardware, reconstruction and analysis when Lorentz Invariance Violation (LIV) studies have to be carried out.