We explored isolated singularities that have finite negative parts of their Laurent series, called poles. We defined the order of a pole and a simple pole as a pole of order 1. We proved a lemma saying that a functions norm goes to infinity near a pole, but when multiplied by a certain power of (z - z_0), the pole turns into a removable singularity. We finished by showing that all singularities of rational functions are removable or poles. Less