The magnetic structure of almandine has been investigated by electronic structure calculations in the local spin density approximation in order to arrive at a more detailed understanding of the magnetic structure and the exchange pathways. The calculations are based on experimentally determined geometrical data of the crystal structure at 100 K. The calculated quadrupole splittings, spin-allowed d – d transitions and magnetic moment for iron atoms are in reasonable agreement with the respective experimental values obtained by Mössbauer and absorption spectroscopy, and magnetization measurements demonstrating the reliability of the calculations. The spin structure is derived from the calculated coupling constants for the possible exchange pathways. The competing superexchange pathways exist via oxygen bridges between directly neighboured iron ions and via edges of silicon tetrahedra and aluminium octahedra connecting more distant iron dodecahedra. Careful consideration revealed that almandine structure contains two identical interpenetrative sublattices of Fe dodecahedra connected via Al octahedra and Si tetrahedra. The calculations provide the information about ferromagnetic interaction between the iron spins within each sublattice, whereas the coupling between two magnetic sublattices is weakly antiferromagnetic via Al octahedra and Si tetrahedra. This antiferromagnetic interaction of two identical magnetic sublattices is in good agreement with the experiments and explains the Mössbauer spectra of almandine below the Néel temperature. Since almandine belongs to most abundant crystallized silicates that are main constituents of the earth and main components of cosmic dust, these results have scientific importance of studying the universe.