During this quantity 3 vital papers of M.G. Krein look for the 1st time in English translation. every one of them is a quick self-contained monograph, every one a masterpiece of exposition. even though of them have been written greater than two decades in the past, the passage of time has no longer diminished their worth. they're as clean and very important as though they'd been written simply the day before today. those papers include a wealth of rules, and should function a resource of stimulation and thought for specialists and newbies alike. the 1st paper is devoted to the idea of canonical linear differential equations, with periodic coefficients. It makes a speciality of the examine of linear Hamiltonian platforms with bounded strategies which remain bounded below small perturbations of the process. The paper makes use of tools from operator idea in finite and limitless dimensional areas and intricate research. For an account of more moderen literature which used to be generated via this paper see AMS Translations (2), quantity ninety three, 1970, pages 103-176 and vital Equations and Operator thought, quantity five, quantity five, 1982, pages 718-757.