We explicitly construct the first nontrivial extractors for degree d \ge 2 polynomial sources over \mathbb{F}_2^n. Our extractor requires min-entropy k\geq n - \frac{\sqrt{\log n}}{(d\log \log n)^{d/2}}. Previously, no constructions were known, even for min-entropy k\geq n-1. A key ingredient in our construction is an input reduction lemma, which allows ... more >>>