  This is an extensive survey of the techniques used to formulate
generalizations of the Mittag-Leffler Theorem from complex analysis. With the
techniques of the theory of differential forms, sheaves and cohomology, we are
able to define the notion of a Mittag-Leffler Problem on a Riemann surface as a
problem of passage of data from local to global, and discuss characterizations
of contexts where these problems have solutions.
