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One service mathematics has rmdcred the 'Et moi, .•.• si j'avait su comment en rcvenir. human race. It has put common sense back je n'y semis point aile.' whc:rc it belongs, on the topmost shcIl next Jules Verne to the dusty callister labc:1lcd 'discarded non­ sense'. The series is divergent; thererore we may be Eric T. Bell able to do something with iL O. Hcavisidc Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com­ puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And alI statements obtainable this way form part of the raison d'etre of this series.

Preface. 1. Averaging in One and Multifrequency Systems of Ordinary Differential Equations. 2. Generalization of Lyapunov's Second Method and Averaging in Stability Theory. 3. Investigation of the Stability of Systems of Ordinary Differential Equations with Quasi-Periodic Coefficients. 4. Investigation of Stability in Multi-Frequency Systems. 5. Investigation of Orbit Stability in the Three Body Problem of Celestial Mechanics Based on the Point Model and on the Model Allowing for Asymmetry in the Distribution of Planet Masses and for the Conservation of Angual Momentum. 6. Investigation of Stability with Account Taken of the Admissible Region of Motions. Investigation of the Stability of a Gyroscope with a No-Contact Suspension. 7. Averaging and Stability Investigation in Systems of Equations with Delay. 8. On Investigation of Stability in Parial Derivative Equations. 9. Investigation of Stability in Stable Systems under Small Random Disturbances. References.