The anomalous Hall effect (AHE) is a transverse voltage that appears in magnetic conductors without an external B-field. Its intrinsic mechanism comes from the Berry curvature Ω(k) of Bloch bands — a geometric property of the wavefunction that acts like a magnetic field in momentum space. The anomalous Hall conductivity is σ_xy = (e²/ℏ)∫_BZ Ω(k) d²k/(2π)², related to the Chern number C. Left panel: Berry curvature over the Brillouin zone (hot = positive, cold = negative flux). Right panel: electron trajectories — the anomalous velocity v_a = (e/ℏ)E×Ω(k) deflects electrons transversely even without Lorentz force. The Chern number is the integral of Berry curvature over the BZ and quantizes the Hall conductance.