Poisson bracket on a smooth manifold M is a bracket on the algebra of
smooth functions satisfying the familiar properties of the Lie bracket,
additionally, a Leibniz identity. I will talk about the history about how
study of classical Hamiltonian mechanics naturally arised a Poisson
bracket of two observable quantities. Basic definitions, relation
between Poisson brackets and Poisson bivectors and Hamilton's equations
of motion and some relevant examples will be included.