This award funds theoretical research in several different topics in relativistic astrophysics and general relativity, with a focus on sources of gravitational radiation that might be detected by the Laser Interferometer Gravitational Wave Observatory (LIGO) and by the proposed space based detector, the Laser Interferometer Space Antenna (LISA). The principal topics are: (A) the development and implementation of methods to compute the gravitational signals from stars or small black holes inspiralling into large spinning black holes; (B) the development of approximation methods to allow highly accurate computations of the gravitational interactions of systems of several bodies, which will be relevant for future tests of general relativity in the Solar System and elsewhere; and (C) computing the experimental constraints on various alternative theories of gravity that have been proposed as explanations for the recently observed acceleration of the expansion of the Universe. The broader impacts of this award are as follows. Education and training of graduate and undergraduate students will be integrated into the research program. The breadth of the research program will be especially beneficial to the graduate students. The training of female graduate students will contribute to gender diversity in the field of relativity (3 of the 7 graduate students the principal investigator has worked with are female). The work on development of computational methods for gravitational waveforms will eventually have a significant impact on gravitational wave astronomy, by enabling the detection and analysis of gravitational wave signals. The principal investigator is taking part in the Speakers Program of the World Year of Physics Speakers Program being organized by the Topical Group in Gravitation of the American Physical Society. As part of this program the principal investigator will give lectures on general relativity to undergraduate institutions. In addition the principal investigator occasionally gives lectures to undergraduate physics majors in small colleges, for example this year at Ithaca College.