Magnetic tunnel junctions (MTJs) are promising candidates for applications in spintronic devices such as magnetic random access memories, read heads and sensors. Previous studies have revealed the critical influence of the chemistry and structure of the ferromagnet metal/alumina interface on both sign and magnitude of the tunneling current in MTJs. We have performed a detailed first-principles study of the structure and bonding at the cobalt/alumina interface in order to understand the relationship between magnetic properties, local bonding environment and cohesion at the interface. Both Al- and 0- terminated interfaces were considered and full geometry optimization of the structure was done by selfconsistent spin-polarized calculations within density functional theory and the generalized gradient approximation. We found that the relaxed atomic structure of the 0-terminated interface is characterized by a rippling of the Co interfacial plane, the average Co-O bond length being 2.04 Å which is within 5% of that in bulk CoO and it is characterized by the covalent bonding between the 0 2p and Co 3d orbitals. The Al-terminated interface contains Co-Al bonds with an average bond length of 2.49 Å compared to 2.48 Å in bulk CoAl and it is characterized by metallic behaviour of the first aluminium layer. As a consequence of different character of bonding, the cohesion at the O-terminated interface is stronger as that at the Al-terminated interface, the work of separation being equal to 6.35 J/m2 and 3.64 J/m2 respectively.