The ordering kinetics of the cylinder phase were characterized using polarizing optical microscopy (POM). Measurements were made on a poly(styrene-b-isoprene) diblock copolymer with block lengths of 15 and 13 kg/mol, respectively, in solution with dibutyl phthalate at a polymer volume fraction of 0.50. Thermal quenches from above the disordering temperature, 39.6 degreesC, to temperatures ranging from 36.5 to 38.4 degreesC allowed for direct observation of nucleation and growth. Two modes of grain growth were observed after nucleation: spherulites and oblate ellipsoids. The ellipsoidal grains had an aspect ratio of 2 and corresponded to single crystals with the cylinders parallel to the minor axis of the ellipsoid. In contrast, the spherulites were polycrystalline, with the cylinder axes predominantly tangential to the spherulite. Ellipsoids and spherulites occurred with comparable frequency at all quench depths. The growth front velocities of individual grains were measured, and the velocities for spherulites and for the major axes of the ellipsoids were approximately twice that along the minor axis of the ellipsoids. The growth front velocities were quantitatively compared to the expression of Goveas and Milner, with good agreement in the temperature dependence. Application of the Avrami equation to the observed ordered fraction yielded parameters in good agreement with those inferred microscopically for heterogeneous nucleation and three-dimensional growth.