The book "Introduction to Relativistic Continuum Mechanics" offers a mathematically oriented introduction to the physics of relativistic continua and thermodynamics within the framework of special relativity. It is aimed at students who should be introduced to these complex topics early on. In addition to classical subjects such as relativistic kinematics and vacuum electrodynamics, the reader is comprehensively introduced to relativistic continuum and fluid mechanics. A central element of the presentation is the 3+1 splitting technique, which is widely used in general relativity and allows for an understanding of the perspective of relative observers. This approach fosters a deep understanding of the physical concepts and their mathematical foundations.