Experimental PAES spectra from the (100) and (111) surfaces of Ge display several strong Auger peaks in the measured energy range corresponding to M4,5N1N2,3 M2,3M4,5M4,5 M2,3M4,5V , and M1M2,3N1,2,3 Auger transitions. Theoretical analysis of PAES data is performed within the modified superimposed-atom method. Positron surface states are computed for both surfaces of Ge. It is found that the positron surface-state wave function is localized mainly on the vacuum side of the topmost layer of Ge atoms. The computed positron binding energies Eb at the (100) and (111) surfaces of Ge are 3.14 and 2.96 eV. In addition, calculations of positron work functions with respect to the vacuum for bulk Ge(100) and Ge(111) yielded 2.77 and 2.85 eV, respecti...