Part 1 - MATHEMATICAL STATISTICS FOR SETI.- Introduction to SETI.- The Drake Equation summarizing five billions years of Evolution in this Galaxy.- The Statistical Drake Equation (SDE).- The Statistical Equation of the Habitables (SHE).- Is there a Galactic Habitable Zone?.- Part 2 - ACTUAL SETI SEARCHES AND STRATEGIES.- Summary of Fifty Years of SETI Searches (1960-2010).- Searching for Beacons in 2010: the Benford's approach.- The Hipparcos Star Catalogue of the Nearest 118,218 Stars in the Galaxy.- The Turnbull-Tarter 'HabCat' Catalogue of the Nearest 17,129 Habitable Stars.- Future Space Missions yielding more Star Catalogues: SIM, GAIA, TPF.- Current SETI Searches from the ground: ATA and the Berkeley SETI Program.- Future SETI Searches from the ground: ATA, LOFAR, ALMA, SKA.- Part 3 - IMPROVING THE SETI SIGNAL PROCESSING BY THE KLT.- A Simple Introduction to the KLT.- KLT from sources in uniform and decelerated motion.- KLT from sources in hyperbolic motion.- KLT from sources in arbitrary motion.- Part 4 - MATHEMATICAL MODELS OF THE PAST FOR EXTRAPOLATION INTO THE FUTURE.- SETI, Exoplanet Searches and Interstellar Flight: When are They Going to Merge?.- Human Expected Lifetime Increase from Upper Paleolithic up to Now and Beyond.- The 'Coral' Model for the Expansion of a Civilization in this Galaxy.- Prospects for Human Interstellar Flight as of 2010.-Trying to Infer Humanity's Future Expansion in the Galaxy on the HabCat basis.