Analytical tools and experimental techniques are developed and used to evaluate the importance of anamorphic gradient-index lens systems in optical design.; A ray trace algorithm is formulated to calculate the paths of rays through anamorphic gradient-index media. The ray trace algorithm is based upon a power series expansion of the ray path and the index profile.; Lenses are designed to couple light from a laser diode into a multimode optical fiber. Designs are formulated for lasers having various amounts of axial astigmatism. A twofold increase in the coupling efficiency beyond that of a butt-coupled system is achieved.; Gradient-index samples having an anamorphic index profile are fabricated using the ion exchange technique. Diffusions into elliptical rods and plane slabs are performed.; An AC shearing interferometer is constructed to measure the index of refraction profile of anamorphic gradient-index samples. Measurements are made of the phase variation across the sheared wavefront. The index of refraction profiles are constructed by numerical integration of the phase data.