This is the first part of a review of research performed in the former USSR. Experimental data were used from several regions of the USSR, including Russia, Ukraine, and Georgia. Many of the publications are available in U.S. libraries. Some of them are translated into English. This part contains results from applying the Complex Dielectric Permittivity method (Dielectric Spectroscopy) for studying the electrical response of rocks in alternating fields with frequencies from 100 Hz to 100 MHz. Data on dielectric properties of sedimentary rocks of different lithology and with various porosities, salinities of saturating solution, and hydrocarbon content are reviewed here. Measurement methods, including means for avoiding or reducing the electrode polarization, are also considered. It is shown that wet rocks exhibit a Maxwell-Wagner polarization process at frequencies 105–107 Hz, caused by charge accumulation on the pore boundaries.