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We describe the Survey for Pulsars and Extragalactic Radio Bursts (SUPERB),an ongoing pulsar and fast transient survey using the Parkes radio telescope.SUPERB involves real-time acceleration searches for pulsars and single-pulsesearches for pulsars and fast radio bursts. We report on the observationalsetup, data analysis, multi-wavelength/messenger connections, surveysensitivities to pulsars and fast radio bursts and the impact of radiofrequency interference. We further report on the first 10 pulsars discovered inthe project. Among these is PSR~J1306$-$40, a millisecond pulsar in a binarysystem where it appears to be eclipsed for a large fraction of the orbit.PSR~J1421$-$4407 is another binary millisecond pulsar; its orbital period is$30.7$ days. This orbital period is in a range where only highly eccentricbinaries are known, and expected by theory; despite this its orbit has aneccentricity of $10^{-5}$.

The SUrvey for Pulsars and Extragalactic Radio Bursts I: Survey Description and Overview