  We present the basic ideas of geometric engineering of the supersymmetric
quantum field theories viewed as a low energy limit of type II strings and
F-theory on singular Calabi Yau manifolds. We first give the main lines of
toric geometry as it is a powerful technique to deal compact complex manifolds.
Then we introduce mirror symmetry which plays a crucial role in the study of
superstring dualities and finally we give elements on Calabi Yau singularities.
After that we study the geometric engineering of N=2 supersymmetric gauge
theories in six and four dimensions. Finally we make comments regarding $ N=1$
SYM in four dimensions.
