The main goal of this new series of conferences is to bring together experts and prominent scientists in order to ensure the exchange of views and experience, as well as to discuss the modern trends in application of mathematics in various fields of engineering, physics, chemistry, economics, biology, etc. The scientific program of the 1st edition of the conference included more than 80 presentations. A number of world renown specialists delivered plenary and key lectures. In addition to the regular session of invited and submitted talks, four special sessions were held as part of the AMiTaNS’09 program. The participation of graduate students was strongly encouraged. During the reviewing process, fruitful discussions occurred between the contributors and anonymous reviewers, which helped the authors improve their contributions essentially. The result of this lively interaction is presented in this volume. The editors hope that publishing these proceedings will serve to promote the application of mathematics in various fields. A wide spectrum of professionals will find something interesting in the collection of papers of 1st AMiTaNS’09.