Ground wires absent from circuits exiting apartment panel
Your building is most likely wired using armored cable (Type AC), so it's grounded, alright
Given the presence of per-conductor paper packing protruding into the panel through the cable connectors, the lack of cable jacketing protruding into the panel through the same route, the lack of ground wires, the vintage of the panel and apparent vintage of the wiring (rather new), and the context of the building and its locale and use (apartment in NYC), my most likely guess as to the wiring method used in your building would be &quot;new style&quot; Type AC (armored cable).  This cable uses the metal armor in conjunction with a thin aluminum bonding strip as the grounding path; the metal cable armor provides a low-resistance path generally, while the bonding strip shorts adjacent turns of the spiral-wound armor to each other to avoid any potential for &quot;choking&quot; of fault currents.  (Very old BX lacked that bonding strip, and there have been various tales of BX armor overheating under low, sustained fault current conditions as a result of the &quot;choke&quot; effect not allowing enough fault current to pass to trip the breaker.)
As an aside: whoever wired that panel was proud of their work, and for the most part deservedly so, so you might as well take this learning opportunity
As an aside, what you are looking at here is a panel that's been quite neatly and professionally wired, by and large.  About the only thing I cannot see in your pictures are the anti-short &quot;redhead&quot; bushings on the connectors. Otherwise, the feeder to this panel looks to be a proper four-wire feed with the panel's bonding screw pulled, as is proper for a subpanel (if this was a main panel, the bonding screw would sit in that &quot;notch&quot; in the top right of the neutral bar).  Furthermore, the branch circuit wiring was done in a very tidy fashion, looping down along the side gutters and back up to the breaker and neutral lugs/screws to provide excess length in case a rearrangement is called for, and all the wiring's been neatly tagged with what circuit it goes to.  Finally, note that all the white wires used as hots in 240V-only circuits, as well as the B leg of the incoming feeder, have been wrapped with red phase tape to prevent confusion.
Best of luck and wishes for your schooling!