The goal of this course is to provide the theoretical basics of continuum mechanics serving as one of the fundamental cores of the COMMAS master program.Therefore,the course content is split into two parts: (I) Mathematical Prerequisites and (II) Continuum Mechanics. In particular, part (I) offers the fundamentals of vector and tensor algebra and analysis. Part (II) deals with the foundations of continuum mechanics including the kinematics, the stress concept and the fundamental balance relations. Finally, the closure problem of continuum mechanics and an application to finite elasticity are presented.