We discuss evolutionary precursors of social intelligence in complex social systems, and dostinguish levels, forms ans types of social intelligence in humans. On the basis of experimental studies of social intelligence in children, we distinguish high, middle and low levels of social intelligence.. The importance of distinguishing levels, forms and types of social intelligence for a number of theoretical and practical issues of preparing a modern child for the effective appropriation of (and functioning in) complex social systems is accentuated.