In an increasingly saturated space about the Earth, aerospace engineers confront the mathematical problem of accurately predicting the position of Earth’s artificial satellites. This is required not only for the correct operation of satellites, but also for preserving the integrity of space assets and the services they provide to citizens. Operational satellites are threatened by the possibility of a collision with a defunct satellite, but most probably by the impact with other uncontrolled man-made space objects—all of them commonly called space debris.The present international concern in space situational awareness (SSA) has produced a renewed interest in analytical and semi-analytical theories for the fast and efficient propagation of catalogs of data. Within this framework, it is widely accepted by experts that perturbation theory based on Lie transforms is the most accurate and efficient method to derive semi-analytical propagators. In a semi-analytical approach, the highest frequencies of the motion are filtered analytically via averaging procedures, allowing the numerical integration of the averaged system to proceed with very long step sizes. Then, the short-period terms can be recovered analytically.Another fundamental need in SSA is the efficient management of uncertainties that characterize the motion of orbiting objects. To this aim Taylor differential algebraic (DA) and Taylor model (TM) techniques have been transferred in the last decade from beam physics field to astrodynamics. These techniques, by allowing high order expansions of the flow of the dynamics and rigorous estimate of the associated approximation errors, have shown to be a powerful tool for managing uncertainties both in initial conditions and model parameters.The focus of this project is to merge Lie perturbation theory and DA and TM techniques with the goal of applying the resulting methodology to practical problems in SSA.