This course provides an introduction to relativistic quantum mechanics and its applications in quantum chemistry. The aim is to develop the subject systematically from the physical foundations of special relativity to practical methods for relativistic electronic structure calculations.

The course begins with the basic concepts of special relativity, including spacetime, Lorentz transformations, relativistic kinematics, and the role of the metric. Building on these ideas, the relativistic description of quantum particles is introduced, leading to the Dirac equation and its interpretation. Particular attention is given to the emergence of spin, the structure of four-component spinors, and the physical origin of relativistic effects in atoms and molecules.

The second part of the course focuses on the formulation of relativistic electronic structure theory. Starting from the four-component Dirac framework, different strategies for obtaining computationally more efficient two-component descriptions are discussed, including relativistic decoupling transformations and the underlying approximations. Effective core potentials (ECPs) are introduced as an alternative approach for incorporating relativistic effects.

A further topic is fermionic symmetry in relativistic quantum mechanics. The course discusses the consequences of time-reversal symmetry, Kramers degeneracy, and the symmetry properties of relativistic spinors, providing the conceptual background for the treatment of many-electron systems in relativistic quantum chemistry. Finally, selected applications illustrate the chemical consequences of relativistic effects and the role of relativistic electronic-structure methods in contemporary computational chemistry. Examples are used to connect the formal theory to observable properties and chemically relevant phenomena.

The course is intended for students with a basic background in quantum mechanics and quantum chemistry. No prior knowledge of special relativity or relativistic quantum mechanics is required.