This volume appears in order to honour the 85th birthday and 65 years of mathematical activities of M. A. Akivis. It was published with the support of the International Geometry Center dω, the Foundation “Science” (Odessa, Ukraine) and the International Conference “Geometry in Odessa – 2008” held in Odessa in May 2008. The volume contains an article “On the occasion of his 85th birthday and 65 years of scientific activity” written by A. T. Fomenko, V. V. Goldberg, V. F. Kirichenko, V. V. Lychagin and A. M. Shelekhov. They describe in more detail results of M. A. Akivis in his three main fields of interest, namely conformal differential geometry, web theory and the theory of local differentiable quasigroups, and projective differential geometry. In the volume, there is also a bibliography of the publications of M. A. Akivis (141 items) and a list of PhD theses (28 of them) written under his supervision. The major part of the volume is devoted to 35 papers of M. A. Akivis. They were chosen by the author himself and he has only included research articles. His survey articles, which are very interesting and important, cannot be found here. Twelve of the articles are in Russian and the other papers are in English.