In this talk we shall take an eclectic tour
through three centuries since the inception of
this function by Euler in 1729. The function
has been the object of intense study by every
great mathematician of the 19th century and
continues to tantalize the modern mathematicians.
We shall dwell upon some of the more important
identities, their modern ramifications and some
new proofs of old results. We shall also discuss
some recent developments that have occured in
the last decade.