The articles in this collection present new results in combinatorics, algebra, algebraic geometry, dynamical systems, analysis, and probability. Of particular interest is the survey article by A. N. Kirillov devoted to combinatorics of Young diagrams and related problems of representation theory. Also included are articles devoted to the eightieth birthday of renowned Russian mathematician, V. A. Rokhlin, ""Remembrances of V. A. Rokhlin"", by I. R. Shafarevich, and ""An Unfinished Project of V.A. Rokhlin"", by V. N. Sudakov. The results, ideas, and methods given in the book will be of interest to a broad range of specialists.