This is a special issue of the journal devoted to the jubilee of the outstanding Ukrainian mathematician, one of the founder of our journal Professor Yuriy Drozd.

Yuriy Drozd was born on the 15th of October, 1944 in Kyiv, in a family of officers, participants of the II World War (his mother was a doctor, his father was an engineer). He was delighted in mathematics still at school, due to his teacher, Asia Aronivna Horon. By the way, three of her former pupils became Doctors of Sciences (the highest scientific degree in the former Soviet Union); it is interesting that all three of them were working in algebra: M.Kargapolov, A.Roiter and Y.Drozd. In 1961 Yuriy got the first prize at the 1st Ukrainian mathematical competition, and at the first All-Russian mathematical competition. The same year he entered Kyiv Taras Shevchenko University, Department of Mechanics and Mathematics. In 1966 he graduated from the University with honours. His advisor at the University was A.Roiter. Collaboration with A.Roiter and V.Kirichenko was a valuable experience of the scientific research for the young mathematician. The main result of his Diploma work (Master Thesis) was a criterion of finiteness of the set of indecomposable representations for cubic rings. It was published in "Proceedings of the Academy of Sciences of the USSR" and was important for the future development of the theory of integral representations of rings.

In 1966 Yuriy Drozd entered a graduate study program at the Institute of Mathematics of the Academy of Sciences of Ukraine. His advisor there was one of the most prominent Soviet mathematicians Igor Shafarevich. In February 1969 Yuriy accomplished his graduate study and since then he was working at the Kyiv Taras Shevchenko University, Department of Mechanics and Mathematics, Division of Algebra and Mathematical Logic. There he followed a long track, form an assistant till a full professor and Head of the Division (1980-1998). In 1970 he presented his Candidate (Ph.D.) Thesis "On Several Questions of the Theory of Integral Representations" at the Steklov Mathematical Institute in Moscow. The results of this thesis, such as a criterion of finiteness of the set of indecomposable representations for commutative orders, structure theory of hereditary and Bassian orders, new results on the structure of genera, took since then a central place in the whole theory of integral representations.

In the following years the scientific interests of Yuriy Drozd broadened. He started his works on a new area, the theory of the so called "matrix problems." Soon he proved one of the main results here, the "tame-wild dichotomy," i.e. the theorem that every finite dimensional algebra is either representation tame or representation wild. This result was the origin of a series of works of specialists through the world. Several conferences were specially devoted to this "tame-wild subject." Yuriy Drozd also implemented the matrix techniques into new areas, such as the multiplicative theory of ideals and others. In 1981 he presented to the Leningrad University his Doctor of Sciences Thesis "Matrix Methods in the Theory of Representations and Rings".

In eighties Yuriy Drozd initiated at the Kyiv University investigations of representations of Lie algebras and groups. In his first paper in this field "On representations of the Lie Algebra sl(2)" he applied matrix methods to study of these representations. Further, in collaboration with S.Ovsienko and V.Futorny, he studied new classes of representations, such as weight representations, Gelfand-Zetlin representations, representations of general position of "mixed" linear groups, etc. Now the achievements of Kyiv mathematicians in these topics are well known and highly appreciated.

The downfall of the USSR and of the Iron Curtain opened a new stage in the scientific biography of Yuriy Drozd. In 1989 he was able for the first time to participate in a scientific conference in the West (it was a meeting of the London Mathematical Society), though he had got invitations to such conferences regularly during more than 15 years before. Further on such visits became usual. From 1992 he was a member of the Scientific Committee of the International Conferences on Representations of Algebras (ICRA), which take place every two years. In 1997 he organized an International Conference on Representation Theory and Computer Algebra in Kyiv.

From 1990 Yuriy Drozd started his fruitful collaboration with his German colleague G.-M.Greuel on investigation of Cohen-Macaulay modules. In about two or three years they completely described representation types of one-dimensional Cohen-Macaulay rings. For Yuriy it was, in a since, a return to his youth, since this topic is a variant of the theory of integral representations of rings. Further they solved the analogous question for vector bundles over projective curves and for a wide class of two-dimensional Cohen-Macaulay rings. Since 1998 Yuriy Drozd started collaboration with another German mathematician, H.-J.Baues, in algebraic topology, which was a completely new area for him. Applying the matrix techniques, they advanced well in classification of stable homotopy types of polyhedra.

These topics led Yuriy Drozd to the theory of derived categories. With his disciples V.Bekkert and I.Burban he extend to these categories the tame-wild dichotomy and gave a complete classification of complexes in derived categories of a wide class of rings as well as for tame projective curves.

Now he is successfully continuing these investigations. They were published in more than 90 papers and served as a basis for 25 Candidate (Ph.D.) Theses of his students (three of them are now Doctors of Sciences). Yuriy Drozd is the author of several University textbooks. Especially the book "Finite Dimensional Algebras" by him and V.Kirichenko was translated by Springer-Verlag into English and is now the most used by students through the world. Yuriy Drozd was a visiting professor at the Universities of Strasbourg, Kaiserslautern, Torun, Santa Barbara, Uppsala. He gave survey talks as invited lector at the international conferences and seminars in Japan, Germany, Great Britain, USA, Canada, France, Mexico, Spain, Brazil.