Dear All, The following preprint, on which my CT2010 and Florence Category Day lectures were based, is available from the Mathematics ArXiv at the address http://front.math.ucdavis.edu/1006.3930: O. Caramello, "The unification of Mathematics via Topos Theory" Abstract: We present a set of principles and methodologies which may serve as foundations of a unifying theory of Mathematics. These principles are based on a new view of Grothendieck toposes as unifying spaces being able to act as 'bridges' for transferring information, ideas and results between distinct mathematical theories. Comments are welcome. Best regards, Olivia Caramello [For admin and other information see: http://www.mta.ca/~cat-dist/ ]