One of the most important factors that determine the state of science potential and, in the long run, the successful results of scientific and technical activity, is its financing. All developed countries conduct an incentive policy to encourage their national science, including systematic support from state budgets for scientific research and technological development. The financing of science in Russia has risen noticeably compared to the time when the institutes did not have enough funds to make rudimentary expenditures and miserly salaries were frequently paid late. Historically, four forms of financing of science have been established: (1) financing of the individual (the scientist); (2) financing of the scientific organization; (3) the financing of science projects by way of a system of grants; and (4) target program financing. All forms of financing are important and essential; the problem is how to find the optimal ratio among them. In regard to the current policy of financing of science in Russia, the authors single out and explore the following basic directions: (1) raising the effectiveness of the utilization of the funds of the federal budget that are channeled into the conduct of research and development; (2) ensuring the priority financing of fundamental research; (3) strengthening the target program method of financing the sphere of research and development; and (4) bringing in additional (alternative) sources for the financing of science. (Contains 3 tables and 8 notes.)