The appearance of the present volume is a truly important event in the world of mathematics. It is a huge step forward for its Hilbert Prize winning author, since he had to overcome the tragedy of the death of his young protégée and co-author, and had to find the strength to complete the work alone. It is important to those who are involved with the organization of mathematical competitions, since they now have more complete access to the problems of the famous Kürschák Mathematical Competition for the years 1947–1963, and the solutions of those problems. Moreover, it is important to those who are engaged in the teaching and/or learning of creative mathematical problem solving, since Andy Liu's Hungarian Problem Book IV is a wonderful vehicle for mastering the process of problem solving in the spirit of the late George Pólya, who was also a product of the Hungarian school of mathematics.

Indeed, Professor Liu's rendition of the problems and solutions of the 51 problems covered in the second half of János Surányi's original Part II of Matematikai Versenytételek is much more than a translation. He groups the problems according to subject matter, develops the background necessary for solving the problems in those areas, and then systematically presents the various solutions, adding several new ones as he proceeds. At the end, he also exemplifies the fourth step of Pólya's process, and reflecting on the solutions of some of the problems, arrives at yet other solutions for some of the other problems. Fortunately, the problems are varied and deep enough to allow for such a treatment at the hands of an expert.