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We report on the background, current status, and current lines of development of the octopus project. This program materializes the main equations of density-functional theory in the ground state, and of time-dependent density-functional theory for dynamical effects. The focus is nowadays placed on the optical (i.e. electronic) linear response properties of nanostructures and biomolecules, and on the non-linear response to high-intensity fields of finite systems, with particular attention to the coupled ionic-electronic motion (i.e. photo-chemical processes). In addition, we are currently extending the code to the treatment of periodic systems (both to one-dimensional chains, two-dimensional slabs, or fully periodic solids), magnetic properties (ground state properties and excitations), and to the field of quantum-mechanical transport or “molecular electronics.” In this communication, we concentrate on the development of the methodology: we review the essential numerical schemes used in the code, and report on the most recent implementations, with special attention to the introduction of adaptive coordinates, to the extension of our real-space technique to tackle periodic systems, and on large-scale parallelization. More information on the code, as well as the code itself, can be found at http://www.tddft.org/programs/octopus/. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)