This volume appears parallel to the conference in honor of Luc Tartar on the occasion of his 60th birthday held in Paris, July 2007 at the CMAP of the Ecole Polytechnique. Partly in collaboration with Fran?ois Murat, Luc Tartar has specialized in the development of new mathematical tools for solving the partial differential equations of continuum mechanics (homogenization, compensated compactness, H-measures), pioneering the study of microstructures...