The variation of the geomagnetic activity index aa over the 138-year interval from 1868 to2005, consisting of 403224 three-hourly values, differs in several aspects from the variation of sunspot numbers over the same interval. Within the framework of the study of Sun-Earth relationships,a spectral analysis is performed to investigate the information inherent in the aa series which monitors the solacorpuscular radiation. The aa spectrum is found to be characterized by distinct lines with associated periods of 90 years, 11 years, 6 months,the daily variation of geomagnetic activity and the harmonics of these fluctuations.The 11-year solar cycle line is largest in amplitude. Although the 11-year peakin the spectrum of the aa index is matched by the sunspotline at the same period,the aa cycle precedes the solar cycle by about 15 months. The semi-annual variation in aa has maxima close to the equinoxes. Since the uncertainty in the dates of the maxima is of the order of a few days, the results support the equinoctial hypothesis for the origin of the semi-annual variation. The aa spectrum is strongly dominated by the broad-band signal in the period range20{40days, related to the variation of the geomagnetic storm recurrence period over a solar cycle. No significant line corresponds to the 27-day rotation of the sun, but there exists onldy a cluster of lines superpsed on an increase of the bzckground noise. There is no explicit evidence for either an annual variation or a line at the lunar synodic period of 29,53 days. The minimum of aa in the declining phase of a solar cycole is shown to be quasi-linearly related to the sunspot maximum of the ,ext cycle. The maximum of the forthcoming solar cycle 24, starting in 2007 AD, is expected to have an annual lean sunspot number of about 130 in 2011 AD, with a rate of ascent to maximum of approximately 36/year abd a subsequent decline to minimum at a rate of about 19/year.