The deepest laws of nature seem to depend on symmetry. After explaining what symmetry is, in its various guises (local, global, exact and approximate), its deepest consequence will be described by Noether's theorem. Its application to mechanics, relativity, the standard model of particle physics and cosmology will be described. We won't be afraid of looking at equations and outlining what they mean but we won't be solving any equations and instead will stick to what the mathematics tells us about reality. Note: There will be no class on 23 Oct; last class on 18 Dec.