  A general procedure for construction of the formalism of quantum beam optics
for any particle is reviewed. The quantum formalism of spin-1/2 particle beam
optics is presented starting {\em ab initio} with the Dirac equation. As an
example of application the case of normal magnetic quadrupole lens is
discussed. In the classical limit the quantum formalism leads to the well-known
Lie algebraic formalism of classical particle beam optics.
