Science plays an important role of development of national economies of developed countries. Post-industrial society, society of knowledge is a society where scientific discoveries, scientific research results ensure economic growth, economic stability, economic exuberance. In such a society not goods, not movable and real property and not natural resources, including power, put together the main society wealth, but scientific discoveries, new knowledge. Countries, which gain primary income from scientific discoveries and high technologies, are prosperous in the modern world. The purpose of study. A solution of science problems in the modern world should become an important direction of a state's attention to providing national security. Weakening of academic and technological as well as technological potential of the country, research reduction, mass closure of research institutes and centres, several-ford reduction in the volume of funding of science, outflow of specialists and intellectual property abroad for the last three years menace Ukraine with a loss of advanced positions in the world, degradation of knowledge-intensive industries, strengthening of external technological dependence and undermining of its defensive capacity. Such a situation predetermined the topic of our research, its main purpose - identification of problems of science financing and determination of ways to solve them. Research methods. When writing the article, a set of methods and approaches was used that allowed realizing a conceptual unity of the research. Dialectical, system, structural methods are used for the analysis of financing of the science advancement in Ukraine, existent problems of the science financing are generalized with the help of comparative and factorial methods; ways for improving financing of the science advancement are determined by using methods of scientific abstraction, synthesis, functional analysis. The results of the study. In Ukraine, a process of reforming of the public sector of science in conjunction with support of new organizational forms, which correspond to market conditions of economy, is declared. It centre around a reduction in this sector, concentration of resources for supporting restricted number of operating research establishments, accelerated liquidation of research institutes, research centres, scientists' reduction, limitation of financial support. National Academy of Sciences of Ukraine is surviving today; there is no link between science and state, science and business, science and enterprises. Scientists are oriented toward grant schemes, cooperation with foreign research centres. The low level of labour remuneration of scientists, outdated equipment, lack of mechanisms to manage scientific research, managerial functions are performed by those who have never done scientific discoveries. An important is keeping scientific organizations, strengthening of links state - science, business - science, enterprise - science; grant of administrative and financing autonomies to scientific structural departments and bodies, developing the system of national research centres, promotion of technological infrastructure of research organizations through the realization of competitive programs for financing of acquisition of modern scientific equipment, increase in wages of scientists according to the European level. Conclusion and discussion position. A foregrounding of financing of the science advancement of Ukraine is possible through the solution of tasks of integration with scientific and innovative space of the European Union, where the strategy "Europe 2020" and main directions of the Fourth Industrial Revolution are being realized successfully. Ukraine has financial resources for the science advancement, there is required a goodwill of politicians who could make effective the links as state - science, business - science, enterprise -science, as well as commercialize new technological solutions.
