In many fields, like fluid dynamics, a large part of the physical systems is described by partial differential equations. They could have prohibitively high dimensions and involve a huge number of unknowns. This makes the computational costs and the memory storage capacity required unaffordable. Therefore, during the last years, some researchers worked at finding mathematical tools of Model Order Reduction (MOR), with the goal of reducing the dimension of the systems thus reducing the computational effort, without simplifying the underlying physics. The key idea is to replace generic approximation spaces by problem specific reduced basis such that they contain the main features of the dynamic systems.