Hitler and the Nazi party used the “science” of Eugenics to substantiate many of the policies and beliefs of their party. Hitler especially utilized this pseudo-science as fact in a number of different ways.

Hitler had read many eugenics books and pamphlets while in prison and he became convinced that only through the application of its principals could Germany become strong. This is where his beliefs on racial hygiene and the idea of the “ubermencht” began. Germany had become weak due to the corruption of the Aryan gene pool and it had to be removed quickly.

Hitler used the ideas of Charles Darwin along with German and Austrian scientists to construct the concept of Social Darwinism, which he would use to legitimize his ethnic cleansing in the later years. Darwin never intended that his ideas regarding Natural Selection be used in such a way, but this idea had already gained traction in Europe.

Hitler later wrote a sequel to Mein Kampf which was never published where he applauded the idea of infanticide that ancient Spartans used to purify their caste. Anyone familiar with the holocaust could see how one led to the other. 

As you can see, eugenics allowed Hitler to substantiate the Nazi racial purity program scientifically.