Beginning with the attempts of Heisenberg and Pauli in the 1920's, the subject grew at an astonishing speed, culminating in the remarkable 
 predictive success of Quantum Electrodynamics. Different attempts to bring the subject to a sound mathematical footing (comparable to that 
 of Quantum Mechanics) -- whether analytic, operator-algebraic or geometric --  have tasted only partial success. These talks will try to  
 give a bird's-eye view of the  mathematical areas (ideas) spawned by these attempts,  keeping in view the recent book of Folland on this 
 subject.