We study two- and three-dimensional matrix Schrodinger operators with <$E m~symbol <174>~bold roman N> point interactions. Using the technique of boundary triplets and the corresponding Weyl functions, we complete and generalize the results obtained by the other authors in this field. For instance, we parametrize all self-adjoint extensions of the initial minimal symmetric Schrodinger operator by abstract boundary conditions and characterize their spectra. Particularly, we find a sufficient condition in terms of distances and intensities for the self-adjoint extension <$E H sub {alpha , X} sup (3)> to have <$E m prime> negative eigenvalues, i.e., <$E kappa sub - (H sub {alpha , X} sup (3))~=~m prime~symbol Г~m>. We also give an explicit description of self-adjoint nonnegative extensions.

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