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 "Advanced Problems in Mechanics" (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.