Chern-Simons theory S = (k/4π)∫ A∧dA is a 3D topological gauge theory whose partition function computes knot invariants. In 2+1D it describes anyons — particles with fractional statistics θ = π/k interpolating between bosons (k→∞) and fermions (k=1). When one anyon winds around another, the wavefunction acquires phase e^{2πi/k}, visible as the Aharonov-Bohm effect from the statistical gauge field. The FQHE (filling ν=1/k) is described by U(1) CS theory at level k; non-Abelian variants (SU(2)_k) underlie topological quantum computing proposals.