Experimental positron annihilation induced Auger electron spectroscopy (PAES) data from Ge(100) and Ge(lll) surfaces display several strong Auger peaks corresponding to M4,5N1N2,3, M 2,3M44,5M4,5, M2,3M4,5V, and M1M4,5M4,5 Auger transitions. The integrated peak intensities of Auger transitions have been used to obtain experimental annihilation probabilities for the Ge 3d and 3p core electrons. The experimental data were analyzed by performing theoretical studies of the effects of surface reconstructions and electron-positron correlations on image potential induced surface states and annihilation characteristics of positrons trapped at the reconstructed Ge(100) and Ge(lll) surfaces. Calculations of positron surface states and annihilation ch...