Learn the fundamental principles of optical lattices in this lecture from the IV School on Light and Cold Atoms. Explore how standing wave patterns of laser light create periodic potentials that can trap and manipulate ultracold atoms, forming artificial crystal structures. Discover the theoretical foundations behind optical lattice systems, including the physics of atom-light interactions, the formation of energy bands, and the emergence of quantum many-body phenomena. Examine how these versatile experimental platforms enable the simulation of condensed matter systems and provide insights into quantum phase transitions, strongly correlated systems, and exotic states of matter. Gain understanding of the mathematical framework used to describe atoms in periodic potentials and the connection between optical lattices and solid-state physics concepts.