Bach proves his mastery of the Baroque concerto here, as in the Brandenburgs -- except this time, we don't have the original music! We do have a harpsichord concerto as well as an organ concerto version of the first movement (which is actually from a cantata)... but we do not have the violin concerto version, which scholars assume must exist. The reason for this assumption is that this music is suited exceptionally well for the violin, and so, this reconstruction was made.
The first six bars of this piece are some of the most dynamic in Baroque music -- if you ever hear someone complain that classical music is "boring", hand them some good headphones and turn this one on!
Another recording of the same piece by Netherlands Bach Society, led by Shunske Sato
Cantata "Wir müssen durch viel Trübsal" (BWV 146) (featuring the source music for this concerto)