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These notes are intended as an elementary introduction to the concept of absolute instability. The transition from convective instability to absolute instability is an important issue when the stability of stationary flow solutions is investigated. The arguments here described were first developed in the framework of plasma physics and later applied to the hydrodynamics of mixing layers and shear flows. Far from being a comprehensive analysis of this complicated subject, the aim of these notes is just to sketch a rudimentary and quite elementary ground for physicists or engineers which have a familiarity with the basic features of linear stability in fluid dynamics, but are new to the concept of absolute instability., Comment: 14 pages, 5 figures