The chapter outlines the research objectives of this thesis and sets the scope of this thesis within the field of gamma-ray astronomy as a tool for studying extreme cosmic phenomena. We discuss how high-energy gamma rays from blazars interact with the extragalactic background light, forming electron-positron pairs that may lose energy through inverse Compton scattering or beam-plasma instabilities. The main focus of this thesis is the investigation of the weak intergalactic magnetic fields’ impact on instability growth and the resulting nonlinear feedback of the electrostatic instability on the pair beams.