The effect of hydrogen on the physical-chemical properties of copper is directly dependent on the types of chemical bonding between H and lattice defects in Cu. In this work, we performed a systematic study of the bonding of H-atoms with crystal lattice defects of copper. This included three types of symmetric tilt grain boundaries (GBs), R3, R5 and R11, and the low Miller index surfaces, (111), (110) and (100). A comparison with literature data for the bonding of H-atoms with point defects such as vacancies was done. From the defects investigated and analyzed, we conclude that the bond strength with H-atoms varies in the decreasing order: surfaces [(111), (110) and (100)] [ vacancy [ R5 GB [ R11 GB [ bulk & R3 GB. A study on the effects of the fcc lattice expansion on the binding energies of H-atoms shows that the main driving force behind the segregation of H-atoms at some GBs is the larger volume at those interstitial GB sites when compared to the interstitial bulk sites.