Dialectics, in the proper sense, is the study of contradiction in the very essence of objects.
Idealist dialectics reached an apex with the work of G.F.W. Hegel around the turn of the 19th-century. Materialist dialectics is at the basis of Marxism.
Karl Marx is quoted defining the difference between his materialist dialectical method and Hegel's idealist dialectical method:
My dialectic method is not only different from the Hegelian, but is its direct opposite. To Hegel, the life process of the human brain, i.e., the process of thinking, which, under the name of “the Idea,” he even transforms into an independent subject, is the demiurgos of the real world, and the real world is only the external, phenomenal form of “the Idea.” With me, on the contrary, the ideal is nothing else than the material world reflected by the human mind, and translated into forms of thought.
The mystifying side of Hegelian dialectic I criticised nearly thirty years ago, at a time when it was still the fashion. But just as I was working at the first volume of it was the good pleasure of the peevish, arrogant, mediocre Ἐπίγονοι [Epigones — Büchner, Dühring and others] who now talk large in cultured Germany, to treat Hegel in same way as the brave Moses Mendelssohn in Lessing’s time treated Spinoza, i.e., as a “dead dog.” I therefore openly avowed myself the pupil of that mighty thinker, and even here and there, in the chapter on the theory of value, coquetted with the modes of expression peculiar to him. The mystification which dialectic suffers in Hegel’s hands, by no means prevents him from being the first to present its general form of working in a comprehensive and conscious manner. With him it is standing on its head. It must be turned right side up again, if you would discover the rational kernel within the mystical shell. - Karl Marx, Afterword to the 2nd German edition of the 1st Volume of Capital[1]