Microtubules are highly dynamic protein polymers that form a crucial part of the cytoskeleton in all eukaryotic cells. Although microtubules are known to self-assemble from tubulin dimers, information on the assembly dynamics of microtubules has been limited, both in vitro and in vivo, to measurements of average growth and shrinkage rates over several thousands of tubulin subunits. As a result there is a lack of information on the sequence of molecular events that leads to the growth and shrinkage of microtubule ends. Here we use optical tweezers to observe the assembly dynamics of individual microtubules at molecular resolution. We find that microtubules can increase their overall length almost instantaneously by amounts exceeding the size of individual dimers (8nm). When the microtubule-associated protein XMAP215 (ref. 6) is added, this effect is markedly enhanced and fast increases in length of about 40-60nm are observed. These observations suggest that small tubulin oligomers are able to add directly to growing microtubules and that XMAP215 speeds up microtubule growth by facilitating the addition of long oligomers. The achievement of molecular resolution on the microtubule assembly process opens the way to direct studies of the molecular mechanism by which the many recently discovered microtubule end-binding proteins regulate microtubule dynamics in living cells.