PLEASE NOTE SPECIAL DAY AND LOCATION:  Talk #1.  In the classical theory of minimal surfaces of the Euclidean space, the better known ones are those with finite total curvature. Laurent Hauswirth and Harold Rosenberg started in 2006 the corresponding theory of complete minimal surfaces with finite total curvature in H2xR, the product space of the hyperbolic plane and the real line. We will give an overview of the subject, including the construction of some examples and classification results.