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The Square Kilometre Array (SKA) is a next-generation radio telescope scheduled to commence construction in 2018. The SKA will be one of a small set of billion-dollar facilities that collectively span the electromagnetic spectrum, and will be an order of magnitude more sensitive than any other radio facility. The SKA's extraordinary survey capacity will allow it to map the distribution of galaxies and large-scale structure over an unprecedented cosmic volume, providing superb probes of dark matter, dark energy, neutrino physics, magnetogenesis, non-gaussianity and inflation. In addition, pulsar timing with the SKA will provide precision tests of general relativity in the strong field regime, and should allow us to detect gravitational radiation produced by merging supermassive black holes. In this talk, I will provide an overview of the capabilities and science goals for the SKA, highlighting its unique potential for advancing our understanding of cosmology and fundamental physics.