Thermal phase transitions, critical exponents, scaling relations, etc, will first be briefly reviewed.

Then quantum phase transitions (QPT) will next be introduced and discussed. To this end, the partition function for quantum systems will be set up and formulated as a path integral leading to a mapping between d-dimensional quantum systems and classical systems in (d+1) dimensions.

This mapping allows for a clear description of QPT and leads to an intimate relation between the dynamics and the statics of the system. It will be illustrated with some specific examples where exact calculations are possible.

More examples of high current research interest will be also discussed.