We describe AlterBBN, a public C program for evaluating the abundances of the elements generated by Big-Bang Nucleosynthesis (BBN). This program enables the user to compute the abundances of the elements in the Standard Model of cosmology, and additionally provides possibilities to alter the assumptions of the cosmological model in order to study their consequences on the abundances of the elements. In particular the baryon-to-photon ratio, the effective number of neutrinos and the neutron lifetime, as well as the expansion rate and the entropy content of the Universe during BBN can be modified in AlterBBN. Such features allow the user to test the cosmological models by confronting them to BBN constraints. A presentation of the physics of BBN and the features of AlterBBN is provided here under the form of a manual.