POLYPAK: An algebraic processor for computations in celestial mechanics. POLYPAK is a package of computer programs for the formal manipulation of real or complex power series in several variables. The program originated in a course on PL/I programming that A. Deprit gave at the University of Cincinnati in 1977. This report is a description of the important features of POLYPAK. POLYPAK has been used in the following research projects: 1. A discussion of entrainment domains for forced second-order differential equations. 2. Formal computation of the limit cycle in van der Pol’s equation. 3. Computation of a formal solution to Hill’s lunar problem with a new way of solving Hill’s differential equation. 4. Computation of the solution to the main problem of lunar theory. 5. Normalization of the Hamiltonian of the restricted problem of three bodies near the Lagrangian equilibrium point L 4 .

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