Rediscovered by J-L LODAY in 1990's, Leibniz algebras are non-anticommutative versions of Lie algebras. In the last three decades numerous papers and results on Leibniz algebras appeared. Leibniz algebras play an important role in different areas of mathematics and physics. In this talk, Lie algebras and Leibniz algebras will be considered from a purely algebraical point of view. In this talk, we will give an introduction to Leibniz algebras, their bimodules and their cohomology. If we have time left, we will describe a special class of Leibniz algebras : the cyclic Leibniz algebras.