In this talk, I will review the basic theory of classical nilpotent orbits, which is a fundamental object at the crossroads of Lie algebras, algebraic geometry, and combinatorics. In particular, I will describe explicitly the simplest nilpotent orbits, attempt to sketch their geometry (nested singularities and Springer fibration), and mention their role in various corners of theoretical physics. The talk is thought of as a pedagogical introduction, with emphasis on concrete examples and very few prerequisites.

IPhT