Complex experimental and theoretical study of the magnetic, magnetoelectric, and magnetoelastic properties of neodymium iron borate NdFe3(BO3)4 along various crystallographic directions have been carried out in strong pulsed magnetic fields up to 230 kOe in a temperature range of 4.2-50 K. It has been found that neodymium iron borate, as well as gadolinium iron borate, is a multiferroic. It has much larger (above 3 10^(-4) C/m^2) electric polarization controlled by the magnetic field and giant quadratic magnetoelectric effect. The exchange field between the rare-earth and iron subsystems (~50 kOe) has been determined for the first time from experimental data. The theoretical analysis based on the magnetic symmetry and quantum properties of the Nd ion in the crystal provides an explanation of an unusual behavior of the magnetoelectric and magnetoelastic properties of neodymium iron borate in strong magnetic fields and correlation observed between them.
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