Space-time metric and Einstein's equations lie at the foundation of general relativity. Somewhat surprisingly, one can start with an SU(2)-gauge theory, write down the simplest equations one can, without making reference to any background field, and show that the Riemannian geometry and Einstein's equations emerge by setting up an appropriate dictionary. Equations of the `fundamental' gauge theory are simple low order polynomials. Complexity of Einstein's equations can be traced back to the fact that the explicit dictionary from the gauge theory to general relativity is rather intricate. The gauge theory framework provides new insights into general relativity, including an interesting interplay between the Lie algebra of volume-preserving diffeomorphisms and the 'integrable' sector of (anti-)self-dual solutions to Einstein's equations. It also leads to a new infinite dimensional Lie algebra that generalizes the Lie algebra of the diffeomorphism group, opening up directions for new mathematical work. I will make a special eort to make the summary of these structures and results accessible to mathematicians as well as physicists.

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