PEPSI is the bench-mounted, two-arm, fibre-fed and stabilized Potsdam Echelle Polarimetric and Spectroscopic Instrument for the 2x8.4 m Large Binocular Telescope (LBT). Three spectral resolutions of either 43 000, 120 000 or 270 000 can cover the entire optical/red wavelength range from 383 to 907 nm in three exposures. Two 10.3kx10.3k CCDs with 9-{mu}m pixels and peak quantum efficiencies of 96 % record a total of 92 echelle orders. We introduce a new variant of a wave-guide image slicer with 3, 5, and 7 slices and peak efficiencies between 96 %. A total of six cross dispersers cover the six wavelength settings of the spectrograph, two of them always simultaneously. These are made of a VPH-grating sandwiched by two prisms. The peak efficiency of the system, including the telescope, is 15% at 650 nm, and still 11% and 10% at 390 nm and 900 nm, respectively. In combination with the 110 m2 light-collecting capability of the LBT, we expect a limiting magnitude of 20th mag in V in the low-resolution mode. The R=120 000 mode can also be used with two, dual-beam Stokes IQUV polarimeters. The 270 000-mode is made possible with the 7-slice image slicer and a 100- {mu}m fibre through a projected sky aperture of 0.74, comparable to the median seeing of the LBT site. The 43000-mode with 12-pixel sampling per resolution element is our bad seeing or faint-object mode. Any of the three resolution modes can either be used with sky fibers for simultaneous sky exposures or with light from a stabilized Fabry-Perot etalon for ultra-precise radial velocities. CCD-image processing is performed with the dedicated data-reduction and analysis package PEPSI-S4S. A solar feed makes use of PEPSI during day time and a 500-m feed from the 1.8 m VATT can be used when the LBT is busy otherwise. In this paper, we present the basic instrument design, its realization, and its characteristics.
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