Abstract
In the previous parts of this thesis, we introduce the basic definitions and theorems of the finite group representation theory. After that we state the classical groups what we need in the last section, e.g. symplectic groups Sp2, and orthogonal groups O2, O3. In the third part, we would list the character tables by the Deligne-Lusztig virtual characters. For the rest, we introduce the Weil representations and find the decompositions of them.