The Continuum Hypothesis says that "Any uncountable subset of the real numbers is equinumerous with all of the real numbers". This statement was first proposed by Cantor in the late 1890's and was considered so fundamentally important that it was listed as the first among Hilbert's famous twenty-three open problems. In 1940 Kurt Godel showed, via his construction of the inner model L, that that the Continuum Hypothesis was consistent with the other axiom of ZFC. However, in 1963, Cohen proved that the Continuum Hypothesis was not just consistent with the axioms of ZFC but was in fact independent of them. His proof made the Continuum Hypothesis the first example of a mathematically important statement which couldn't be decided by the standard axioms of set theory. The methods used in showing the independence of the continuum hypothesis gave rise to several of the most important ideas in modern set theory. In this series of talks we will introduce these important ideas and prove the independence of the Continuum Hypothesis from ZFC In the first half of this series we will introduce Cohen's method of forcing and use this method to show that the Continuum Hypothesis can't be proved from the other axioms of set theory.