  This paper gives an overview of several key innovations in the 19th century
which led to complex geometry in the 20th century. This includes the creation
of the complex plane, the work of Abel on addition theorems for generalized
elliptic integrals, the theory of elliptic functions, holomorphic functions,
and the creation of Riemann surfaces by Riemann in the mid 19th century. A
number of the original papers which contain these new ideas are looked at in
some detail and a detailed set of references is included.
