  The problem of construction of the boundary conditions for the Toda lattice
compatible with its higher symmetries is considered. It is demonstrated that
this problem is reduced to finding of the differential constraints consistent
with the ZS-AKNS hierarchy. A method of their construction is offered based on
the B\"acklund transformations. It is shown that the generalized Toda lattices
corresponding to the non-exceptional Lie algebras of finite growth can be
obtained by imposing one of the four simplest integrable boundary conditions on
the both ends of the lattice. This fact allows, in particular, to solve the
problem of reduction of the series $A$ Toda lattices into the series $D$ ones.
Deformations of the found boundary conditions are presented which leads to the
Painlev\'e type equations.
  Key words: Toda lattice, boundary conditions, integrability, B\"acklund
transformation, Lie algebras, Painlev\'e equations

Exactly Solvable and Integrable Systems;Exactly Solvable and Integrable Systems