Hydrodynamic stability is a fascinating field in the fluid mechanics, that deals with the transition of laminar flow to turbulence. In fact, this field discloses the originofinstabilityandleadstothephysicalmechanism. Italsounveilsavari- ety of complex phenomena on the fluid surface including the emergence of pri- mary and secondary waves and their behaviors in various physical conditions when the controlling flow parameters alter. More specifically, hydrodynamic instability enables us to decipher the rationale of complex waves appeared in different regimes of flow parameter. The study of hydrodynamic instability was initiated in the beginning of 19th century.