Trajan's Market is part of a huge complex known as Trajan's Forum, built by the "good Emperor" Trajan (53-117).
The complex of the imperial fora, was designed by Apollodorus of Damascus, and dedicated in A.D. 113.
A large piazza in the complex, is centered by the large Column of Trajan,
originally flanked on either side Greek and Latin libraries.

The Market can be visited, and has been greatly restored in some parts ,wth rooms containing statuary and objects
of interest such as amphora, remains of bronze sculpture, etc.
Much that would be of interest seems to be closed to visitors, and apparently used as offices for the complex.