The role of Mechanics in governing key biological processes at the cell scale is becoming increasingly apparent. At the interface between biology, biophysics, and mechanics, Mechanobiology is emerging as a new, thriving research field, that is attempting to understand Biology from the perspective of Mechanics. And while the key role played by biochemical regulation in molecular cell biology is undisputed, the importance of forces and stresses in determining how cells function is becoming more and more widely recognised. Forces control shape and motion of the cells. But also how cells decide when and how much to differentiate, and where cells migrate to (e.g., durotaxis). Unveiling the details of this mechano-transduction opens the way to understanding key biological process at the cell scale first, and then at the tissue and organ scale. Cell motility provides one concrete example where Mechanics is shaping our understanding of key biological processes. More generally, Mechanics is providing us with a conceptual framework to go beyond the identification of the molecular components and their individual function, by integrating them into a comprehensive understanding of cell motion and migration, of cell and tissue morphogenesis. The course will survey recent advances in the fields of cell motility and Mechanobiology of cells and tissues, emphasising such an integrative approach. The topics of this Advanced School, which builds upon a previous one organised in 2014 by M. Arroyo and A. DeSimone, will include cell migration on solid substrates, adhesion and control of shape and migration, scaffold design in tissue engineering, mechanics of neural network growth, statistical mechanics and energetics of single cells, and mechanics of the cytoskeleton with an emphasis on its role in detecting and responding to mechanical, topological, and chemical cues. Both theoretical aspects (mathematical and computational modelling) and experimental techniques will be surveyed. The Course will consist of 7 introductory lectures by the organisers, of 23 lectures on more specialised topics given by four eminent experts in the field, and of 4 “perspectives” lectures that will open and close the Course. In addition, a poster session will be organised, together with a social evening, to allow participants to discuss topics related to their research or professional interests. The financial support from the European Research Council, through the ERC Advanced Grant 340685-MicroMotility, and the endorsement by the Italian Association for Theoretical and Applied Mechanics (AIMETA) are gratefully acknowledged.