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Let $A$ be an algebra with fixed set of generators $a_1,\dots,a_s$. $V_A(n)$be dimension of the space, generated by worlds of length $\le n$ over $a_i$,$T_A(n)=V_A(n)-V_A(n-1)$. If $T_A(n)<\mbox{Const}$, algebra $A$ is a {\itboundary algebra}. We describe a normal basis of boundary algebras, i.e.algebras with small growth.  Let $\cal L$ be a factor language over alphabet $\cal A$. {\it Growthfunction} $T_{\cal L}(n)$ is number of subwords $\cal L$ of degree $n$. Wedescribe factor languages of small growth such that $T_{\cal L}(n)\len+\mbox{const}$.

Describtion of normal basis of boundary algebras and factor languages of small growth