It is well known that a lens-based far-field optical microscope cannot resolve two objects beyond Abbe's diffraction limit. Recently, it has been demonstrated that this limit can be overcome by lensing effects driven by surface-plasmon excitation(1-3), and by fluorescence microscopy driven by molecular excitation(4). However, the resolution obtained using geometrical lens-based optics without such excitation schemes remains limited by Abbe's law even when using the immersion technique(5), which enhances the resolution by increasing the refractive indices of immersion liquids. As for submicrometre-scale or nanoscale objects, standard geometrical optics fails for visible light because the interactions of such objects with light waves are described inevitably by near-field optics(6). Here we report near-field high resolution by nanoscale spherical lenses that are self-assembled by bottom-up integration(7) of organic molecules. These nano-lenses, in contrast to geometrical optics lenses, exhibit curvilinear trajectories of light, resulting in remarkably short near-field focal lengths. This in turn results in near-field magnification that is able to resolve features beyond the diffraction limit. Such spherical nanolenses provide new pathways for lens-based near-field focusing and high-resolution optical imaging at very low intensities, which are useful for bio-imaging, near-field lithography, optical memory storage, light harvesting, spectral signal enhancing, and optical nano-sensing.