This book focuses on original theories and approaches in the field of mechanics. It is based on several lectures of the 50th Anniversary of the International Summer School-Conference "e;Advanced Problems in Mechanics"e; (June 2022, St. Petersburg, Russia), and with an emphasis on problems and solutions at the boundaries between mechanics and other areas of research. The respective chapters highlight cutting-edge work that promotes development in fields like micro- and nanomechanics, materials science, solid state physics, molecular physics, astrophysics, and many others.