The study of abelian manifolds forms a natural generalization of
the theory of elliptic functions, that is, of doubly periodic
functions of one complex variable. When an abelian manifold is
embedded in a projective space it is termed an abelian variety in
an algebraic geometrical sense. This introduction presupposes
little more than a basic course in complex variables. The notes
contain all the material on abelian manifolds needed for
application to geometry and number theory, although they do not
contain an exposition of either application. Some geometrical
results are included however.
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