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We consider effects of Coulomb interaction in a granular normal metal at notvery low temperatures suppressing weak localization effects. In this limitcalculations with the initial electron Hamiltonian are reduced to integrationsover a phase variable with an effective action, which can be considered as abosonization for the granular metal. Conditions of the applicability of theeffective action are considered in detail and importance of winding numbers forthe phase variables is emphasized. Explicit calculations are carried out forthe conductivity and the tunneling density of states in the limits of large$g\gg 1$ and small $g\ll 1$ tunnelling conductances. It is demonstrated for anydimension of the array of the grains that at small $g$ the conductivity and thetunnelling density of states decay with temperature exponentially. At large $g$the conductivity also decays with decreasing the temparature and itstemperature dependence is logarithmic independent of dimensionality andpresence of a magnetic field. The tunnelling density of states for $g\gg 1$ isanomalous in any dimension but the anomaly is stronger than logarithmic in lowdimensions and is similar to that for disordered systems. The formulae derivedare compared with existing experiments. The logarithmic behavior of theconductivity at large $g$ obtained in our model can explain numerousexperiments on systems with a granular structure including some high $T_{c}$materials.Comment: 30 page

Coulomb effects in granular materials at not very low temperatures