THE development of techniques for focusing X-rays has occupied physicists for more than a century. Refractive lenses, which are used extensively in visible-light optics, are generally considered inappropriate for focusing X-rays, because refraction effects are extremely small and absorption is strong. This has lead to the development of alternative approaches(1,2) based on bent crystals and X-ray mirrors, Fresnel and Bragg-Fresnel zone plates, and capillary optics (Kumakhov lenses). Here we describe a simple procedure for fabricating refractive lenses that are effective for focusing of X-rays in the energy range 5-40 keV. The problems associated with absorption are minimized by fabricating the lenses from low-atomic-weight materials. Refraction of X-rays by one such lens is still extremely small, but a compound lens (consisting of tens or hundreds of individual lenses arranged in a linear array) can readily focus X-rays in one or two dimensions. We have fabricated a compound lens by drilling 30 closely spaced holes (each having a radius of 0.3 mm) in an aluminium block and we demonstrate its effectiveness bg focusing a 14-keV X-ray beam to a spot size of 8 mu m.