The solid-electrolyte interphase (SEI) is probably the least understood component in Li-ion batteries. Considerable effort has been put into understanding its formation and electrochemistry under realistic battery conditions, but mechanistic insights have mostly been inferred indirectly. Here we show the formation of the SEI between a graphite anode and a carbonate electrolyte through combined atomic-scale microscopy and in situ and operando techniques. In particular, we weigh the graphitic anode during its initial lithiation process with an electrochemical quartz crystal microbalance, which unequivocally identifies lithium fluoride and lithium alkylcarbonates as the main chemical components at different potentials. In situ gas analysis confirms the preferential reduction of cyclic over acyclic carbonate molecules, making its reduction product the major component in the SEI. We find that SEI formation starts at graphite edge sites with dimerization of solvated Li+ intercalation between graphite layers. We also show that this lithium salt, at least in its nascent form, can be re-oxidized, despite the general belief that an SEI is electrochemically inert and its formation irreversible.