Cu2ZnSnS4 (briefly CZTS) belongs to a family of quaternary chalcogenide semiconductors, which attracts considerable attention in recent time due to a high potential of photovoltaic applications. Indeed, besides of an efficiency up to 12.6 % of solar cells, based on CZTS (doped with Se) [1], this compound exhibits presence of only low-cost, low-toxic and abundant elements in the crust.Electronic properties of CZTS are influenced strongly by a mixed kesterite-stannite structure [2], leading to a high intrinsic lattice disorder. The latter is accompanied by a deep acceptor level with energy EA ~ 120  140 meV of the main CuZn defects [3,4]. These features expand considerably (up to T between ~ 50  150 K) the interval of the Mott variable-range hopping (VRH) transport [5]. However, the nature of CZTS conduction mechanisms beyond this range still has not acquired a sufficient understanding, whereas even the resistivity data below 10 K are lacking in literature.Here, we have investigated resistivity,  (T), and magnetoresistance (MR) of CZTS single crystals within a broad interval of T ~ 2  300 K in pulsed magnetic fields up to B = 20 T to obtain information on the charge transfer mechanisms and microscopic properties of charge carriers.The Mott VRH conduction over the states of the defect acceptor band (AB) with width W has been observed within the same interval of T ~ 50  150 K as in Ref. 5 above, and the obtained data of W ~ 12  25 meV support those of Ref. 5, too. The joint analysis of  (T) and MR (which is positive at any T and B) have yielded a series of microscopic parameters, such as density of the localized states, positions of the Fermi level and mobility thresholds in the AB. The values of the localization radius, a  22  45 Å, have been found to depend on proximity to the metal-insulator transition.On the other hand, the Shklovskii-Efros VRH conduction [6] has been observed below T ~ 3  4 K. Here, the behavior of MR changes drastically, exhibiting a pronounced anomalous character [7]. This is accompanied by a dramatic increase of the localization radius a  50  170 Å. Both anomalies above have been explained quantitatively by a constructive interference of different paths, arising from multiple scattering of hopping carriers at low temperatures [8]. In particular, the low-temperature values of the localization radius, evaluated in frames of the theory of interference phenomena in the VRH conduction [8], exhibit a reasonable agreement with the experimental data.This work was supported by projects IRSES PVICOKEST 269167, IRSES MAGNONMAG 295180 and STCU 5985, as well as by the Institutional Project CSSDT 15.817.02.04A.[1] W. Wang, M. T. Winkler, O. Gunawan, T. Gokmen, T. K. Todorov, Y. Zhu, and D. B. Mitzi, Adv. Energy Mater. 4 (2014) 1301465.[2] S. Schorr, H.-J. Hoebler, and M. Tovar, Eur. J. Mineral 19 (2007) 65.[3] Shiyou Chen, Ji-Hui Yang, X. G. Gong, Aron Walsh, and Su-Huai Wei, Phys. Rev. B 81 (2010) 245204.[4] S. Levcenko, V. E. Tezlevan, E. Arushanov, S. Schorr, and T. Unold, Phys. Rev. B 86 (2012) 045206.[5] K. G. Lisunov, M. Guk, A. Nateprov, S. Levcenko, V. Tezlevan, and E. Arushanov, Sol. Energ. Mater. Sol. Cells 112 (2013) 127. [6] B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors (Springer, Berlin, 1984).[7] B. I. Shklovskii, Sov. Phys. Semicond. 17 (1983) 1311.[8] B. I. Shklovskii and B. Z. Spivak, Scattering and interference effects in variable range hopping conduction, edited by M. Pollak and B. Shklovskii (North-Holland, Amsterdam, 1991).