NOVELTY - Method (I) of fabricating an aspherical gradient refractive index (GRIN) lens comprises: co-extruding a first polymer material having a first refractive index and a second polymer material having a second refractive index different than the first refractive index to form multilayered polymer composite films; assembling the multilayered polymer composite films into a multilayer composite GRIN sheet; and shaping the multilayered composite GRIN sheet into an aspherical lens.    USE - The method is useful for fabricating GRIN lens, which is useful: in imaging applications (small camera applications including camera phones, surveillance cameras, medical imaging tools (e.g. endoscopes), and military imaging (e.g. scopes and space cameras); non-image forming systems (energy collection devices, solar cells, solar collectors, solar concentrators and beam shaping devices); and for producing biological implants, preferably devices that are implantable as optical materials to improve damaged or deteriorating human vision.    ADVANTAGE - The method: utilizes the multilayered polymer composite films that allows to easily achieve any predetermined index gradient, and thus provides the fabricated GRIN lens, which exhibits an index gradient of greater than or equal to 0.01, or 0.02-1, preferably 0.05-0.5, and has an aspherical shape that adds to the correct power of the GRIN distribution to correct wavefronts for spherical and other higher order aberrations, and further the aspheric surface curvatures have the ability to modify optical wavefronts and correct for spherical or higher order aberrations inherent to commercial glass and plastic monolith lens materials, thus allowing for larger corrections of lens aberrations and production of unique optics with performance unachievable with spherical surfaces; and increases the design freedom on the lenses to reduce the overall size and weight of the optical system in which the lens is used.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are also included for:    (1) a gradient index lens, comprising a co-extruded, multilayered composite GRIN sheet having an aspherical shape, where the multilayered composite sheet includes many stacked co-extruded multilayered polymer composite films, each including many of at least two alternating layers (A) and (B) of formula (AB)x, where layer (A) is comprised of component (a) and layer (B) is comprised of component (b), and the components (a) and (b) have different refractive indexes;    (2) a method (II) of fabricating the gradient index lens, comprising: fabricating the multilayered composite GRIN sheet by forming a set of multilayered polymer composite films comprising the alternating layers (A) and (B); assembling the films into a multilayered composite GRIN sheet; and forming the gradient index lens by slicing and shaping the multilayered composite GRIN sheets into an aspherical shape; and    (3) an aspherical gradient index lens, comprising a co-extruded, multilayered composite GRIN sheet that includes many stacked co-extruded multilayered polymer composite films, where the sheet defines an oblate ellipse, which has a first half-parabolic GRIN distribution, and a prolate ellipse, which has a second half-parabolic GRIN distribution, through the lens thickness.    x = 2(n); and    n = 4-18.