  Symmetries are playing a very prominent role in natural sciences. In
mathematics as the language of physics, symmetries are treated within the
framework of group theory, which provides the tools to classify natural laws
and physical objects like elementary particles. The present work discusses
aspects of relativistic quantum field theory as the mathematical theory of
particle physics which are relevant for the modern description of elementary
particles and their associated fields hitherto considered as fundamental
building blocks of the theory. Due to the abstract nature of quantum field
theory, these aspects can only be touched by their exemplification within a
review.
