An introduction to magnetic geometry

Magnetic systems are a well-known class of classical Hamiltonian systems, serving as a fundamental model for the motion of a charged particle on a Riemannian manifold under the influence of a magnetic force. They were first formalized by V. Arnold in the 1980s, and in recent decades,  they have been actively investigated by numerous mathematical communities. Through many examples, this talk aims to provide a straightforward overview of both classical and recent developments in the theory. A particular focus will be placed on the new concept of magnetic curvature, and, if time permits, I will also present some new applications that can be derived from it. The presentation is designed to be accessible and requires no prior background, making it suitable for audiences of all types.