  We first recall two equivalent definitions of Lie $2$-algebras,
categorification of Lie algebras and $2$-term $L_\infty$-algebras. Then we
present four different kinds of Lie $2$-algebras from $2$-plectic manifolds,
Courant algebroids, homotopy Poisson manifolds and affine multivector fields on
a Lie groupoid respectively. Moreover, we recall the cohomology theory of Lie
$2$-algebras and analyze its lower degree cases. The integration of strict Lie
$2$-algebras to strict Lie $2$-groups is also discussed.
