The article under review is devoted to finding estimates for the level of some finite-dimensional solvable Lie algebras [for more detail, see the author's articles, Izv. Vyshch. Uchebn. Zaved. Mat. 1992, No. 10 (353), 19-27 (1992; Zbl 0753.17002) and Algebra Anal. 5, No. 3, 100-118 (1993; Zbl 0798.17021)]. The author studies the action of the group \(GL_n(K)\) on the space \(\Lambda_n(K)\) of all \(n\)-dimensional Lie algebras over a field \(K\). Let \(O_n(L)\) be the orbit of an algebra \(L\) and let \(\overline{O}_n(L)\) be its closure in the Zariski topology (or in the Euclidean topology for \(K={\mathbb C}\)). Write \(L \rightarrow L'\) (the Lie algebra \(L'\) is called a contraction of the Lie algebra \(L\)) if \(L'\in\overline{O_n}(L)\) and write \(L \Rightarrow L'\) (the Lie algebra \(L'\) is called a degeneration of the Lie algebra \(L\)) if \(L'\oplus A'\in\overline{O}_n(L\oplus A)\) for some abelian algebras \(A\) and \(A'\). The level of a Lie algebra \(L\in\Lambda_n(K)\) is the maximal length of a chain \(L=L_0\Rightarrow L_1 \Rightarrow \ldots\) . In the first section, \(2\)-nilpotent Lie algebras and their levels are studied. Some lower estimates are obtained for the level of \(2\)-nilpotent Lie algebras and for arbitrary finite-dimensional Lie algebras. Let \(L\) be a solvable Lie algebra. The author calls \(L\) splitting if it decomposes into the semidirect sum \(L=A\dotplus N\) of a nilradical \(N\) and an abelian subalgebra \(A\) whose action on \(N\) by means of the adjoint representation is semisimple. An arbitrary finite-dimensional Lie algebra is called splitting if so is its radical. In the second section, splitting Lie algebras are considered and, in the third section, solvable Lie algebras of the shape \(L=K\dotplus_{\phi}K^{n-1}\) are studied, where \(\phi: K\mapsto gl_{n-1}(K)\) is some linear mapping determining the decomposition of \(L\) into a semidirect sum (the author calls such Lie algebras almost abelian). Some lower and upper estimates are given for the level of almost abelian Lie algebras. A criterion is obtained for existence of degeneration of a Lie algebra of this type into another such algebra.