The main manifestations of solar activity, such as sunspots, floccules and
faculae are described. A short history of research on the Sun’s activity from Galileo and
Scheiner to modern times is presented. The main instrumental solar indexes - Wolf
number, group sunspot number, sunspot area - and their general statistical laws
(Gnevyshev-Ohl rule, Waldmeier rule etc.) are described. Up-to-date modern
knowledge of major solar periodicities (cycles of Schwabe, Hale, Gleissberg etc.) and
global extremes of solar activity (Maunder and Spörer minima, Medieval maximum
etc.) are discussed. Moreover, some major phenomena related to space weather (solar
wind, aurora borealis etc.) and other terrestrial manifestations of solar activity are
considered. Modern methods of statistical analysis of non-stationary time series,
including Fourier, wavelet, and singular spectrum analyses, long-range correlation
analysis and multi-fractal approach are introduced. A method used for the evaluation of
significance in details of wavelet spectra is presented. Furthermore, some enduring
problems are shortly described.
Keywords: Solar activity, solar-terrestrial relationship, space weather.
