  In this series of lectures directed towards a mainly mathematically oriented
audience I try to motivate the use of operator algebra methods in quantum field
theory. Therefore a title as ``why mathematicians are/should be interested in
algebraic quantum field theory'' would be equally fitting. Besides a
presentation of the framework and the main results of local quantum physics
these notes may serve as a guide to some frontier research problems in
mathematical physics with applications in particle and condensed matter physics
for whose solution operator algebraic methods seem indispensable. The
ultraviolet problems of the standard approach and the recent holographic
aspects belong to this kind of problems.
