The purpose of this project is to investigate magneto-optical fingerprints of altermagnetism. The computational resources will support theoretical calculations aimed at identifying characteristic optical signatures of altermagnetic order. Altermagnets are an emerging class of quantum materials that combine compensated magnetic order with non-relativistic spin-split electronic bands, offering a promising platform for spin-based quantum technologies without macroscopic magnetization. Harnessing this potential, however, requires new approaches to identify, read out and control their unconventional magnetic order and its associated spin-dependent electronic states. This work will establish nonlinear magneto-optics as a sensitive interface to altermagnetic quantum materials. Our central hypothesis is that nonlinear optical responses provide symmetry-selective fingerprints of altermagnetism, directly encoding its magnetic order parameters and characteristic momentum-dependent spin splitting. We will investigate how these microscopic properties govern spin-induced second harmonic generation (SHG), nonlinear photo-currents and multiphoton resonances, and identify optical observables that can distinguish altermagnetic order and its different symmetry classes. By combining first-principles calculations and effective microscopic models, we will develop a joint theory-experiment approach to establish direct connections between microscopic spin configurations, magnetic multipoles and experimentally accessible nonlinear optical signals, providing new strategies for optical readout of altermagnetic states.