In these thesis we show, using the Weierstrass theorem, that every entire function can be represented as a product of functions, from which we can easily identify zeros of the function. We also show that for any given sequence without accumulation points, we can construct a holomorphic functions with zeros of prescribed order at exactly the points in the sequence. Next we present Mittag-Leffler's theorem, that similarly shows that, for any sequence without repetitions and without accumulation points, we can construct meromorphic functions that have prescribed finite principle Laurent parts at exactly the points in the sequence. In the end, we show the usefulness of proved theorems on concrete examples.
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