Low-weight amyloid-β (Aβ) oligomers formed at early stages of oligomerization rather than fibril assemblies seem to be the toxic components that drive neurodegeneration in Alzheimer’s disease. Unfortunately, detailed knowledge of the structure of these early oligomers at the residue level is not yet available. In this study, we performed all-atom explicit solvent molecular dynamics simulations to examine the oligomerization process of Aβ_10–35 monomers when forming dimers, trimers, tetramers and octamers, with four independent simulations of a total simulated time of 3 μs for each oligomer system. The decomposition of the stability free energy by MM-GBSA methodology allowed us to unravel the network of energetic interactions that stabilize such oligomers. The contribution of the intermonomeric van der Waals term is the most significant energy feature of the oligomerization process, consistent with the so-called hydrophobic effect. Furthermore, the decomposition of the stability free energy into residues and residue-pairwise terms revealed that it is mainly apolar interactions between the three specific hydrophobic fragments 31–35 (C-terminal region), 17–20 (central hydrophobic core) and 12–14 (N-terminal region) that are responsible for such a favourable effect. The conformation in which the hydrophobic cthr–chc interaction is oriented perpendicularly is particularly important. We propose three other model substructures that favour the oligomerization process and can thus be considered as molecular targets for future inhibitors. Understanding Aβ oligomerization at the residue level could lead to more efficient design of inhibitors of this process.