Various algorithms for normalizing autonomous Hamiltonian systems are considered: for expanding a Hamiltonian in a Taylor series, and for linear and non-linear normalization. The number of degrees of freedom of the Hamiltonian system and order of normalization are arbitrary. It is assumed that all the eigenvalues of the matrix of the linearized system are purely imaginary and there are no resonances up to second order inclusive, that is, there are no equal or zero frequencies in the system. The most economical algorithms for use in analytic computation systems as regards computer memory are described and implemented in a software package written in the REDUCE language. This software can be used for all the analytical calculations arising from computer normalization of autonomous Hamiltonian systems.