This book offers a vision of how evolutionary life processes can be modelled. It presents a mathematical description that can be used not only for the full evolution of life on Earth from RNA to modern human societies, but also the possible evolution of life on exoplanets, thus leading to SETI, the current Search for ExtraTerrestrial Intelligence.   The main premise underlying this mathematical theory is that the Geometric Brownian Motion (GBM) can be applied as a key stochastic process to model the evolution of life. In the resulting Evo-SETI Theory, the life of any living thing (a cell, an animal, a human, a civilization of humans, or even an ET civilization) is represented by a b-lognormal, i.e., a lognormal probability density function starting at a precise instant (b, birth) then increasing up to a peak time, then decreasing to senility time and then continuing as a straight line down to the time of death. Using this theory, Claudio Maccone arrivesat remarkable hypotheses on the development of life and civilizations, the possibility of extraterrestrial life, and when computers will take over the reins from us humans (Singularity). The book develops the mathematical Evo-SETI Theory by integrating a set of articles that the author has published in various journals on Astrobiology and Astronautical Research.