  This paper is the first in a series of three, the aim of which is to lay the
foundations of algebraic geometry over the free metabelian Lie algebra $F$. In
the current paper we introduce the notion of a metabelian Lie $U$-algebra and
establish connections between metabelian Lie $U$-algebras and special matrix
Lie algebras. We define the $\Delta $-localisation of a metabelian Lie
$U$-algebra $A$ and the direct module extension of the Fitting's radical of $A$
and show that these algebras lie in the universal closure of $A$.
