This volume contains mainly the lectures delivered by the participants of the International Conference: Operator Theory and its Applications in Mathematical Physics - OTAMP 2004, held at Mathematical Research and Conference Center in Bedlewo near Poznan. The idea behind these lectures was to present interesting rami'cationsofoperatormethodsincurrentresearchofmathematicalphysics.The topicsoftheseProceedingsareprimarilyconcernedwith:functionalmodelsofn- selfadjointoperators,spectralpropertiesofDiracandJacobimatrices,Dirichlet-to- Neumann techniques, Lyapunovexponents methods and inversespectral problems for quantum graphs. All papers of the volume contain original material and were refereed by - knowledged experts. The Editors thank all the referees whose critical remarks helped to improve the quality of this volume. The Organizing Committee of the conference would like to thank all session organizers for taking care about the scienti'c programm and all participants for making warm and friendly atmosphere during the meeting. Weareparticularygratefultotheorganizersof SPECT,withoutwhose'n- cial support the OTAMP 2004 would never been so successful. We also ackno- edge'nancialsupportofyoungPolishparticipantsbyStefanBanachInternational Mathematical Center and thank the sta? of the Conference Center at Bedlewo for their great support which helped to run the conference smoothly.

Finally, we thank the EditorialBoardand especially ProfessorI. Gohberg for including this volumeinto the seriesOperator Theory:Advances and Applications and to Birkhauser ¨ -Verlag for help in preparation of the volume.