  We describe all locally semisimple subalgebras and all maximal subalgebras of
the finitary Lie algebras $\gl(\infty), \sl(\infty), \so(\infty)$, and
$\sp(\infty)$. For simple finite--dimensional Lie algebras these classes of
subalgebras have been described in the classical works of A. Malcev and E.
Dynkin.
  Key words (2000 MSC): 17B05 and 17B65.
