Could humans build a city on the Moon?

Yes — humans could probably build a city on the Moon in principle, but it would be a very difficult, long-term engineering project rather than anything like a normal Earth city.

The biggest hurdles are:

• Radiation and vacuum: The Moon has no atmosphere or magnetic field, so habitats would need heavy shielding, likely from regolith cover, underground construction, or lava tubes.
• Extreme temperatures: Lunar surface temperatures swing wildly, so buildings and systems would need strong thermal control.
• Water and air: A city would need a reliable source of water and oxygen, likely by mining polar ice where it exists and processing it.
• Materials and construction: Launching everything from Earth would be far too expensive, so settlers would need to use lunar resources as much as possible.
• Power: A city would need dependable energy through the long lunar night, probably from a mix of solar power, storage, and possibly nuclear power.
• Dust: Lunar dust is sharp, abrasive, and hard to manage, so equipment and habitats would need special protection.

So the short answer is: yes, probably — but only as a heavily engineered, self-contained settlement, and likely not a large self-sustaining city for a long time. Permanent human presence is something various lunar programs have discussed for the 2030s, but a sprawling city with many civilians would likely be much farther off.