  Properties of partial integrals such as real and complex-valued polynomial,
multiple polynomial, exponential, and conditional for ordinary differential
systems are studied. The possibilities of constructing first integrals and last
multipliers by known partial integrals are considered. Applications of partial
integrals to solve the Darboux problem and to the extended Darboux problem are
given. Integral basis of the Jacobi system is built. And the inverse problem of
constructing differential systems on the base of their partial integrals is
solved.
