This thesis proposes a robust dynamic observer for linear systems to output disturbances or sensor malfunctions. The propose robust dynamic observer can simultaneously estimate the system state and the output disturbances. The dynamic observer in this thesis has new observer structure, the robust dynamic observer design problem can be transformed into a disturbance rejection control problem. One can then apply the frequency shaping design in disturbance rejection to the robust observer design. The frequency shaping ensures both stability and performance of the robust dynamic observer. Previous output disturbance observer mostly requires that the open-loop system be stable, while the robust dynamic observer has no such constraint.