Luna Habitats
There is no air on the Moon. And the temperature varies from 387 degrees Fahrenheit BELOW zero (-233 Celsius) at night to 253 degrees Fahrenheit ABOVE zero (123 Celsius) in the day. Tiny micro-meteoroids (space rocks) rain down on the Moon's surface. And no atmosphere means no protection from the Sun's harsh radiation.
So a Luna habitat for humans will have to be very tough and very sturdy. It will have to be air tight, so the inside can be pumped up with breathable air without exploding or leaking. The habitat will have to be cooled during the Moon day and heated during the Moon night. It will need a water recycling system, a power generating system, and food storage and preparation facilities.
Lava tubes
An important possibility is that of using Lava tubes.
The surface of the Moon experiences severe temperature changes. In the daytime, the surface can heat up to 127 C and cool to -173 C at night. But observations from NASA's Lunar Reconnaissance Orbiter show that inside collapsed lava tubes on the Moon, the temperature always remains a comfortable 17 C. You could wear a short-sleeved shirt (inside a pressurized space suit) and wouldn't need complex and power-hungry heaters and coolers. In the low gravity of Mars, these lava tubes can be hundreds or even thousands of meters tall, allowing room for enormous lunar bases.
These long, winding lava tubes are like structures we have on Earth. They are created when the top of a stream of molten rock solidifies and the lava inside drains away, leaving a hollow tube of rock.