The GALLEX experiment for the detection of solar neutrinos by means of a radiochemical gallium detector is operated by groups from Italy, France, Germany, Israel and the USA in the Gran Sasso underground laboratory (LNGS) near L'Aquila (Italy). It consists of (i) the technical scale tank made of glass fiber reinforced polyester fabric containing 101 tonnes (54 m3) of a highly concentrated (8 moll-1) GaCl3 solution; (ii) a gas sparging system for desorption of GeCl4 which has been formed by interaction of the neutrinos with gallium according to71Ga +ν e →71Ge + e- and by addition of ca. 1 mg of a stable Ge isotope; (iii) the absorption columns for concentration of GeCl4 into a volume of 1 l of water; (iv) the laboratory scale apparatus for conversion of GeCl4 to GeH4 and mixing with the counting gas Xe; (v) the counter filling station, and (vi) the low level proportional counters. Contributions of possible side reactions which have to be corrected for, e.g. by cosmic muons, fast neutrons andα-emitters are discussed, as well as the purification of the target solution from long-lived (t 1/2 = 271 d) cosmogenic68Ge. A first preliminary result after one year of solar neutrino measurement is presented. This constitutes the first direct measurement of the basic proton-proton fusion reaction in the core of the sun. This result, appreciably below the predictions of the standard solar model (SSM) (132 SNU) can be interpreted, together with the results of the chlorine and KAMIOKANDE experiments either by astrophysics or by neutrino oscillations (MSW effect). The solar neutrino measurements are continuing and a calibration experiment with a51Cr source is in preparation.