This talk will be a brief introduction to zeta function techniques in the       
computation of naively divergent quantities as they arise in several             
important calculations in quantum mechanics, quantum field theory and string    
theory. After illustrating the method in the simple case of the so-called       
Casimir effect in quantum field theory, I will define generalized zeta          
functions and their associated heat kernels, and use them to compute the        
determinant of a simple differential operator.