Structural and energetic properties of hydrogen bonded infinite chains and of two-dimensional infinite periodic networks of formamide molecules were investigated by the ab initio crystal orbital method using several, partly highly polarized, atomic basis sets of increasing size at the Hartree-Fock (HF) level and by including electron correlation effects in different orders of Moller-Plesset (MP) perturbation theory, up to the complete MP4 level. For comparison, calculations at the same theoretical levels were also performed for the monomer and for dimers in three different configurations (linear, zig-zag, and cyclic). Besides full structural optimizations, the intermolecular interaction energies were corrected for basis set superposition errors taking into account monomer relaxation effects as well. The results show that hydrogen bonding in the formamide crystal is a highly cooperative phenomenon, both from the structural and energetic points of view. The lengths of the hydrogen bonds, R(HB) will be reduced by 0.12-0.18 Angstrom in the crystalline environment, as compared with dimers, both for HF and MP theories and the binding energies will be increased typically by 50%-60%. Electron correlation effects substantially influence the structural features (reducing, e.g., R(HB) by about 0.08-0.10 Angstrom) and contribute 15%-20% to the cohesion energy. The theoretical model explains why the R(HB) values for open-chain dimers become shorter in the crystal than those obtained for the cyclic ones (as opposed to free dimers), correctly predicts changes of bond lengths in going from the monomer to the crystal, and provides N-H ... O bond lengths and lattice constants very close to experiments.