Wide-angle optical functionality is beneficial for imaging and image projection devices. Conventionally, wide-angle operation is attained by a complicated assembly of optical elements. Recent advances have led to meta-surface lenses or meta-lenses, which are ultra-thin planar lenses with nanoantennas that control the phase, amplitude, and/or polarization of light. Here, we present a meta-lens capable of diffraction-limited focusing and imaging over an unprecedented >170° angular field of view (FOV). The lens is integrated on a one-piece flat substrate and includes an aperture on one side and a single meta-surface on the other side. The meta-surface corrects third-order Seidel aberrations, including coma, astigmatism, and field curvature. The meta-lens has a planar focal plane, which enables considerably simplified system architectures for imaging and projection. The meta-lens design is generic and can be readily adapted to different meta-atom geometries and wavelength ranges to meet diverse application demands.