The extrapolation of track parameters and their associated covariances to destination surfaces of different types is a very frequent process in the event reconstruction of high energy physics experiments. This is amongst other reasons due to the fact that most track and vertex fitting techniques are based on the first and second momentum of the underlying probability density distribution. The correct stochastic or deterministic treatment of interactions with the traversed detector material is hereby crucial for high quality track reconstruction throughout the entire momentum range of final state particles that are produced in high energy physics collision experiments. This document presents the main concepts, the algorithms and the implementation of the newly developed, powerful ATLAS track extrapolation engine. It also emphasises on validation procedures, timing measurements and the integration into the ATLAS offline reconstruction software
