There are several problems in PDE where tools from harmonic  
analysis are extremely useful.  In increasing generality, the concepts  
of Fourier multipliers, pseudodifferential operators, and Fourier  
integral operators have all found uses in PDE.  The goal of the talk  
will be to motivate the study of these tools using examples from PDE,  
and to then prove some basic results to give an idea of how they work.