Density functional theory is a very important method for calculating ground-state properties for atoms, molecules and solids. Albeit exact in principle, its implementation requires an approximation for the so-called exchange-correlation energy. The most popular of these approximations, the local-density and generalized-gradient approximations, are local or semi-local and do not include the highly non-local van der Waals interaction.<p /> In this thesis a density functional for calculating the asymptotic van der Waals interaction energy for objects of different sizes and geometries is proposed. It is based on the adiabatic-connection formula for the exchange-correlation energy, where two basic approximations are made. First, the density response function is calculated at the level of the random phase approximation. Second, a local approximation is made for the screened response.<p /> In practice a doubly local approximation for the dielectric function is used when evaluating the interactions, together with a cutoff of each interacting object. This real-space cutoff prevents spurious overestimates of the response in the density tails otherwise caused by the local approximation. Explicit forms of the functional are derived for three model systems --- interacting atoms or molecules, an atom or molecule outside a surface and finally two interacting surfaces. Also the derivation of a correction to the 1 / z<sup>2</sup>-dependence for the asymptotic interaction between two surfaces is accounted for.<p /> The functional is applied to and found very reasonable for a number of different objects, such as atoms, fullerenes, and other molecules. Surfaces at different levels of approximation are treated successfully, from jellium surfaces to low-indexed Al surfaces calculated within a plane-wave pseudopotential code, with both surface structure and relaxation of the outermost atomic layers. Anisotropic effects for interacting molecules and molecules outside a surface are also considered.<p /> In summary, this thesis demonstrates that it is indeed possible to restore van der Waals interactions in density functional theory. An explicit van der Waals density functional that is proposed for long-ranged interactions is successfully applied to a range of test cases with mutual interactions of atoms, molecules, and surfaces. The prospects for a working van der Waals functional, applicable to problems within solid state physics, chemistry, and biology look very good
