We study the usual one-dimensional Kondo lattice model (1D KLM) using
the non-Abelian bosonization. At half filling, we obtain a Kondo insul
ator with a gap in both charge and spin excitations that varies quite
linearly with the Kondo exchange J(K). It consists Of a spin-density g
lass state, or a q = pi spin density wave weakly pinned by a nearly an
tiferromagnetically ordered spin array. We will study the stability of
this Kondo insulator against both quenched disorder and interactions
between conduction electrons. Away from half filling, the metallic sys
tem now yields a very small spin gap that is equal to the one-impurity
Kondo gap T-k((imp)). Unlike the one-impurity Kondo model, we will sh
ow that this Kondo phase cannot rule the fixed-point of the 1D KLM, aw
ay from half filling. We rather obtain a heavy-fermion metallic state
controlled by the energy scale T-coh(proportional to)(T-k((imp)))(2)/t
(t is the hopping term) with a quite long-range antiferromagnetic pol
arization. [S0163-1829(98)00539-6].