This is the ?rst of two volumes containing peer-reviewed research and survey papers based on invited talks at the International Conference on Modern Analysis and Applications. The conference, which was dedicated to the 100th anniversary ofthebirthofMarkKrein,oneofthegreatestmathematiciansofthe20thcentury, was held in Odessa, Ukraine, on April 9-14, 2007. The conference focused on the main ideas, methods, results, and achievements of M. G. Krein. This?rstvolumeisdevotedtotheoperatortheoryandrelatedtopics. Itopens withthebiographypapersaboutM. G. Kreinandanumberofsurveypapersabout his work. The mainpartof the book consistsof originalresearchpaperspresenting the state of the art in operator theory and its application. The second volume of these proceedings, entitled Di?erential Operators and Mechanics, concerns other aspects of the conference. The two volumes will be of interest to a wide-range of readership in pure and applied mathematics, physics and engineering sciences. The editors are sincerely grateful to the persons who contributed to the preparation of these proceedings: Sergei Marchenko, Myroslav Sushko, Kostyantyn Yusenko and Vladimir Zavalnyuk.Mark Grigorievich Krein, 1907-1989 Operator Theory: Advances and Applications, Vol. 190, xi-xx c 2009 Birkh. auser Verlag Basel/Switzerland Mark Grigorievich Krein (on his 100th birthday anniversary) V. M. Adamyan, D. Z. Arov, Yu. M. Berezansky, V. I. Gorbachuk, M. L. Gorbachuk, V. A. Mikhailets and A. M. Samoilenko April 3, 2007, is the l00th anniversary of the birth of Mark Grigorievich Krein, one of the most celebrated mathematicians of the 20th century, whose whole life was closely connected with Ukraine.