The reconstruction of the trajectories of charged particles, or track
reconstruction, is a key computational challenge for particle and nuclear
physics experiments. While the tuning of track reconstruction algorithms can
depend strongly on details of the detector geometry, the algorithms currently
in use by experiments share many common features. At the same time, the intense
environment of the High-Luminosity LHC accelerator and other future experiments
is expected to put even greater computational stress on track reconstruction
software, motivating the development of more performant algorithms. We present
here A Common Tracking Software (ACTS) toolkit, which draws on the experience
with track reconstruction algorithms in the ATLAS experiment and presents them
in an experiment-independent and framework-independent toolkit. It provides a
set of high-level track reconstruction tools which are agnostic to the details
of the detection technologies and magnetic field configuration and tested for
strict thread-safety to support multi-threaded event processing. We discuss the
conceptual design and technical implementation of ACTS, selected applications
and performance of ACTS, and the lessons learned.