This master thesis deals with the Stokes and the Navier-Stokes problem in a reduced order framework and its extension to uncertainty quantification. After their success in computational fluid dynamics, one of the problems that emerged is that often the numerical simulations take too much computational time. Usually these problems are relevant when the equations depend on some physical/geometrical parameters and we are interested in the solution for several such parameters, as in the many-query problems or real-time simulation problems. In these cases the finite element method or finite volume method, called full order method, are too slow and we need something faster.