The atmosphere of a planet is very important for the determination of its climate. As we know well the atmospheric composition may change with time causing the climate to change on historical time scale (i.e., in a few tens of years) as it is happening at the present time due to the increasing abundance of the greenhouse gases mixing ratios. Considering the drastic changes in the composition of the atmosphere, the distribution and extension of the continents we expect to find a corresponding evolution in the climate of the Earth. There is an additional variable related to the astrophysical factor and that is that our Sun follows a luminosity evolution typical of its star class which makes it roughly 5% brighter every Ga. That makes the output of the star 30% lower when the Solar System was born. However even with such decrease in the solar output evidence shows that on our planet still had temperature which permitted the survival of life forms. This corresponds to the so-called Faint Young Sun Paradox that was discovered by Carl Sagan and George Mullen more than 50 years ago. First of all we will ask how we can assert the environmental conditions on such distant past and then follow possibly the evolution of the climate of the Earth until the present epoch.