1. Introduction
2. The classical pseudo-differential Weyl calculus on $\mathbb{R}^{n}$
3. Weyl calculus for irreducible unitary representations
3.1. Preduals for coadjoint orbits
3.2. Weyl calculus for unitary irreducible representations
4. Magnetic Weyl calculus on nilpotent Lie groups
4.1. Magnetic Weyl calculus
4.2. Magnetic Moyal product