  Motivated by the sharp contrast between classical and quantum physics as
probability theories, in these lecture notes I introduce the basic notions of
operator algebras that are relevant for the algebraic approach to quantum
physics. Aspects of the representation theory of C*-algebras will be motivated
and illustrated in physical terms. Particular emphasis will be given to
explicit examples from the theory of quantum phase transitions, where concepts
coming from strands as diverse as quantum information theory, algebraic quantum
physics and statistical mechanics agreeably converge, providing a more complete
picture of the physical phenomena involved.
