We report on the first observation of nonlinear Faraday rotation with cold atoms at a temperature of ∼100 µK. The observed nonlinear rotation of the light polarization plane is up to 0.1 rad over the 1 mm size atomic cloud in approximately 10 mG magnetic field. The nonlinearity of rotation results from long-lived coherence of ground-state Zeeman sublevels created by a near-resonant light. The method allows for creation, detection and control of atomic superposition states. It also allows applications for precision magnetometry with high spatial and temporal resolution. PACS numbers: 33.57.+c, 42.50.Dv, 42.50.Gy, 32.80.Xx The linear Faraday rotation (LFR) of the polarization plane of light propagating in the medium is a well known consequence of optical anisotropy caused by a longitudinal magnetic field. For thermal gases the Doppler effect broadens the range of the magnetic fields where the effect is visible and reduces the size of the maximum rotation relative to atoms at rest. The use of cold atoms with their Doppler width narrower than the natural linewidth distinguishes this situation from experiments at room temperature. The experiments on LFR with cold atoms were performed in a magneto-optical trap (MOT) [1][2][3], and in an optical dipole trap [4].Application of strong, near-resonant laser light may result in the creation of coherent superpositions of Zeeman sublevels of an atomic ground state. Such superpositions (Zeeman coherences) are known to be responsible for a variety of coherent phenomena in lightmatter interaction, like coherent population trapping [5], electromagnetically-induced transparency [6], nonlinear magneto-optical rotation or nonlinear Faraday rotation (NFR) [7] and their interplay [8]. Superposition states are also at the heart of quantum-state engineering (QSE). Most of QSE experiments require initial states of well defined atomic spin (or total angular momentum F ), usually prepared in a stretched state, which is realized by putting most of (ideally all) atomic population into a Zeeman sublevel with extreme value of magnetic quantum number m [9]. Below we report how superpositions of specific Zeeman sublevels, or Zeeman coherences belonging to a given F are created in cold (∼100 µK) atomic samples and observed with high sensitivity using nonlinear Faraday rotation. In the experiment laser light both creates and detects the Zeeman coherences. The same detection technique can be applied to detect the presence of Zeeman coherences already introduced with other mechanisms. Furthermore, the time-dependent detection provides information on the temporal evolution of the superposition states.The described experiment shows the potential of NFR with cold atoms for precision magnetometry with prospective µG sensitivity, large dynamic range (zerofield to several G), and sub-mm spatial resolution in magnetic field mapping. Magnetic field sensing with cold atoms utilizing Larmor precession of alkali atoms in a magnetic field has been discussed in: MOT [10], Bose-Einstein condensate [11,12] and ...