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The annual Operator Theory conferences, organized by the Department of Mathematics of INC REST and the University of Timi?oara, are intended to promote cooperation and exchange of information between specialists in all areas of operator theory. This volume consists of papers contributed by the participants of the 1984 Conference. They reflect a great variety of topics, dealt with by the modern operator theory, including very recent advances in the invariant subspace problem, subalgebras of operator algebras, hyponormal, Hankel and other special classes of operators, spectral decompositions, aspects of dilation theory and so on. The research contracts of the Department of Mathematics of INCREST with the National Council for Science and Technology of Romania provided the means for developing the research activity in mathematics; they represent the generous framework of these meetings, too. It is our pleasure to acknowledge the financial support of UNESCO which also contibuted to the success of this meeting. We are indebted to Professor Israel Gohberg for including these Proceedings in the OT Series and for valuable advice in the editing process. Birkhauser Verlag was very cooperative in publishing this volume. Mariana Bota, Camelia Minculescu and Rodica Stoenescu dealt with the difficult task of typing the whole manuscript using a Rank Xerox 860 word processor; we thank them for the excellent job they did.