  Let $L$ be an algebra over a field $F$ with the binary operations $+$ and
$[,]$. Then $L$ is called a left Leibniz algebra if it satisfies the left
Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,c\in
L$. A linear transformation $f$ of $L$ is called an endomorphism of $L$, if
$f([a,b])=[f(a),f(b)]$ for all elements $a,b\in L$. A bijective endomorphism of
$L$ is called an automorphism of $L$. It is easy to show that the set of all
automorphisms of the Leibniz algebra is a group with respect to the operation
of multiplication of automorphisms. The description of the structure of the
automorphism groups of Leibniz algebras is one of the natural and important
problems of the general Leibniz algebra theory. The main goal of this article
is to describe the structure of the automorphism group of a certain type of
nilpotent three-dimensional Leibniz algebras.
