To form an up-to-date picture of what is going on in a given area of mathematics, we usually consult a shelf of current periodicals or, to save time, the appropriate section of a reviewing journal. Thus we learn of new advances in the area, which problems have been solved, what progress has been made with others, while rarely, and then only in the context of the author's own results, do we learn which problems the author failed to solve but considers interesting. In all this, a summary of current problems has no less a place in the development of a subject than a list of achievements, though the apparent connection between the two is often deceptive. Thus, it is desirable to publish from time to time a summary of important problems with the participation of a large circle of authors. The Kourovka notebook is such a collection of unsolved problems in group theory.
The current edition is the seventh, the first having appeared in 1965. Chapter 7 is entirely new; the first six chapters are reproduced from the sixth edition with slight editorial changes. The comments on the problems have been reviewed and augmented.
Experience shows the benefits of collecting problems of interest in a given area. Of the 422 problems in the sixth edition, 151 have now been solved.
