Context : Full-disk solar flux spectra can be directly compared to stellar spectra and thereby serve as our most important reference source for , for example stellar chemical abundances , magnetic activity phenomena , radial-velocity signatures or global pulsations . Aims : As part of the first Potsdam Echelle Polarimetric and Spectroscopic Instrument ( PEPSI ) key-science project , we aim to provide well-exposed and average-combined ( viz . deep ) high-resolution spectra of representative stellar targets . Such deep spectra contain an overwhelming amount of information , typically much more than what could be analyzed and discussed within a single publication . Therefore , these spectra will be made available in form of ( electronic ) atlases . The first star in this series of papers is our Sun . It also acts as a system-performance cornerstone . Methods : The Sun was monitored with PEPSI at the Large Binocular Telescope ( LBT ) . Instead of the LBT we used a small robotic solar disk integration ( SDI ) telescope . The deep spectra in this paper are the results of combining up to \approx 100 consecutive exposures per wavelength setting and are compared with other solar flux atlases . Results : Our software for the optimal data extraction and reduction of PEPSI spectra is described and verified with the solar data . Three deep solar flux spectra with a spectral resolution of up to 270,000 , a continuous wavelength coverage from 383 nm to 914 nm , and a photon signal to noise ratio ( S/N ) of between 2,000-8,000:1 depending on wavelength are presented . Additionally , a time-series of 996 high-cadence spectra in one cross disperser is used to search for intrinsic solar modulations . The wavelength calibration based on Th-Ar exposures and simultaneous Fabry-Pérot combs enables an absolute wavelength solution within 10 m s ^ { -1 }  ( rms ) with respect to the HARPS laser-comb solar atlas and a relative rms of 1.2 m s ^ { -1 }  for one day . For science demonstration , we redetermined the disk-average solar Li abundance to 1.09 \pm 0.04 dex on the basis of 3D NLTE model atmospheres . We detected disk-averaged p-mode RV oscillations with a full amplitude of 47 cm s ^ { -1 } at 5.5 min . Conclusions : Comparisons with two solar FTS atlases , as well as with the HARPS solar atlas , validate the PEPSI data product . Now , PEPSI/SDI solar-flux spectra are being taken with a sampling of one deep spectrum per day , and are supposed to continue a full magnetic cycle of the Sun .