One of the most fundamental symmetries in physics is CPT invariance. This series of lectures will review the CPT theorem with particular attention to the ingredients needed for the proof. Two versions of the proof, the original Lagrangian-based approach as well as the axiomatic approach, will be sketched and the close connection to Lorentz symmetry will be highlighted. The presentation of the proofs will be followed by a discussion of the major physical implications that arise from CPT invariance, in particular the equality in magnitude of various physical properties of a particle and its antiparticle. Motivated by recent theoretical and experimental interest in CPT tests, various approaches to the violation of CPT invariance will be mentioned, and it is outlined how they evade the CPT theorem. Examples of CPT-violation searches with particular focus on the Standard-Model Extension test framework will be delineated. An attempt will be made to keep this lecture series self-contained and at a level suitable for a broad audience by excising as many technical aspects as possible.