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Single-walled carbon nanotubes are ideal systems for investigating fundamental properties and applications of one-dimensional electronic systems. The interaction of magnetic impurities with electrons confined in one dimension has been studied by spatially resolving the local electronic density of states of small cobalt clusters on metallic single-walled nanotubes with a low-temperature scanning tunneling microscope. Spectroscopic measurements performed on and near these clusters exhibit a narrow peak near the Fermi level that has been identified as a Kondo resonance. Using the scanning tunneling microscope to fabricate ultra-small magnetic nanostructures consisting of small cobalt clusters on short nanotube pieces, spectroscopic studies of this quantum box structure exhibited features characteristic of the bulk Kondo resonance, but also new features due to finite size.