This dissertation gives a panorama of contemporary epistemology and present philosopher Karl Paul Feyerabend s ideas on the progress of science. We attempt to address mainly the following topic: what are the thoughts of a philosopher on scientific progress who sees science as an enterprise of anarchy and without a foundation? In our attempt at providing an answer, we make a historical reconstruction of the cultural atmosphere in which Feyerabend was involved and of his philosophical career. This reconstruction shows the conditions that produced the Vienna Circle, which influenced many thinkers at the time who were concerned with the subjects of science and progress, like Popper, Kuhn, Lakatos and Laudan. These philosophers will have their epistemologies briefly analyzed since they were important in the formation of Feyerabendian thought. We conclude with a defense of epistemological anarchism as we contend that the subject of science s progress in Feyerabend should be understood from the bases of this doctrine.