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This is a slightly shortened version of a lecture given at the tercentenary Euler meeting Euler's mathematical legacy held in Oxford in June 2007. It describes some of Euler's work on what later became known as zeta functions and L-functions, and explains why this work remains of fundamental importance in modern number theory.
1From a later point of view this is the Dirichlet L-function for the unique non-trivial character of the group (.
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