In this talk we will present several classical results on finite-dimensional Leibniz algebras. We give main examples of Leibniz algebras and show nilpotency of Leibniz algebras in terms of special kinds of derivations. Also, we present the structure of solvable Lie algebras with a given nilradical and with the maximality condition for the complementary subspace to the nilradical. Moreover, among such solvable Lie algebras we shall indicate a subclass of Lie algebras whose cohomology group is trivial. Finally, we provide some examples of infinite-dimensional Lie algebras with a similar structure.