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We describe the concept of the spin‐polarized scanning tunneling microscope. It consists of a ferromagnetic tip with saturated magnetization from which spin‐polarized electrons tunnel into a ferromagnetic sample which has its axis of magnetization aligned with that of the tip. When the magnetization of the sample is alternated periodically from parallel to antiparallel, a portion of the tunnel current is predicted to oscillate at the same frequency, with an amplitude linearly proportional to the average tunnel current. The construction of a prototype microscope, operated in air, is described. When the sample magnetization is alternated, a modulation of the tunnel current is observed at the same frequency. This signal satisfies criteria developed to characterize spin‐polarized tunneling. Spurious signals are also observed and their probable origins identified. A number of improvements are suggested that should eliminate the spurious effects.