The current paper opens a series of papers that are aimed at the determination of barriers that govern the covalent coupling between partners of C 60-based composites consisting of two or more fullerenes C 60 (C 60 dimer and oligomers) (Part 1), C 60 and single-walled carbon nanotube ([C 60+4,4)] carbon nanobud) (Part 2), and C 60 and graphene ([C 60+(5,5)] and [C 60+(9,8)] graphene nanobuds) (Part 3). C60 dimers and oligomers are considered in the current paper. The formation of composites is considered from the basic points related to the regioselective chemical reactivity of the fullerene molecule atoms. The dissonance between the predicted trimer and tetramer structures and experimental observations is suggested to evidence the topological nature of the C 60 oligomerization. The barrier that governs the oligomer formation is determined in terms of the coupling energy E cpl tot and is expanded over two contributions that present the total energy of deformation of the composites’ components E def tot and the energy of covalent coupling E cov tot. The computations were performed by using the AM1 semiempirical version of unrestricted broken symmetry Hartree-Fock approach.