In this work we describe the design and implementation of an optical system that enables the study of the interactions of Rydberg atoms or other Rydberg species in well-defined geometries. To understand and observe the dynamics of Rydberg interactions, the ability to engineer different arrangements of microscopic cold atom traps and manipulate their positions with a precision of a few microns is essential. This is accomplished by a custom designed high-numerical-aperture long-working-distance objective lens and a spatial light modulator device to control the phase of an incoming optical beam. Several different trap geometries have been realized, with a spatial resolution of a few microns, including a 1-dimensional chain, a 2-dimensional square grid, and a circular array of traps. The objective lens has been designed to provide diffraction limited performance at multiple wavelengths facilitating the creation of not only micron-scale atom traps but also the fluorescence imaging of trapped atoms. The system enables precise control over trap positions, and hence the locations at which atoms might be excited, with applications in, for example, the study of long-range interactions between Rydberg atoms, the creation of long-range Rydberg molecules, the implementation of qubits for quantum computing based on Rydberg atoms, and in quantum simulation.