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There is a growing interest in the connection of a single molecule or a wire of atomic diameter between two electrodes. This has led to the investigation of a new class of nanoscale materials: lines of metal atoms of atom-sized cross section, lines of atomic defects, and conjugated oligomers. Several ways to fabricate such materials are discussed, such as the self assembly of metal atoms on a surface under UHV, deposition from or sliding with an STM tip apex, and local surface modification using a voltage pulse. The synthesis of molecular wires is also presented, the objective being to produce long, low-gap, rigid conjugated oligomers. §The electrical connection of a single atomic or a single molecule is more challenging: Mechanical (break junction) STM or nanolithographic coplanar junctions are currently being used to measure the resistance of a single nanometer-scale wire. The theoretical problems associated with such measurements involve both solid state physics and quantum chemistry.