The first part of a collaborative survey of the linear and nonlinear optical properties of silver thiogallate, carried out by the Centre National d\´Etudes des Télécommunications (Bagneux) and the Department of Electronics of the University of Southampton, is presented. A detailed study of second-harmonic generation (SHG) in silver thiogallate is presented. Careful experiments in the near and medium infrared lead to a new determination of the coefficient

. Comparison is made with previously published values. Crystal quality is discussed and the nature of the visible twinning defects elucidated.