Well first, you could fill a crater, or cover the surface with a breathable liquid. Can Humans Breathe Liquid? Though I’m not sure if this is quite feasible and safe yet. Also, apart from ionic fluids (which have a very low vapour pressure, proposed for liquid mirror telescopes on the Moon), even high molecular weight fluids evaporate in a vacuum. So you’d need to cover it with something to keep the liquid from evaporating. It might be a fun idea to explore in science fiction.

However, with light gases oxygen and nitrogen such as we have on Earth, it is possible to give the Moon an Earth pressure atmosphere temporarily. It depends how long you want it to last.

A thin atmosphere vanishes quickly, on the order of a year or two, through the impact of particles from the solar wind blowing it away.

But a thick atmosphere could last much longer, because the upper atmosphere protects the lower atmosphere. This is from: An Atmosphere for the Moon

Here are a few rough calculations based on the figures there:

Only about 10^8 kg a year would be carried away by the solar wind. The Moon has a surface area of 3.79 million square kilometers, or 3.79*10^12 square meters. At ten tons per square meter, that would weigh 3.79*10^16 kg.

So, losing 10^8 kg a year, it would last for nearly four million years before it is all completely gone. It would take 100,000 years to lose a tenth of the atmosphere.

That’s an atmosphere with a sixth of the Earth’s pressure in the lower lunar gravity. For full Earth pressure 1 bar you’d need six times as much, 60 tons of material per square meter, and it would take 600,000 years to lose a tent of its atmosphere.

The original paper he refers to here is by Richard Vondrak et al, and is from the 1970s. See Page 342. He calculates that it would be possible to create a breathable atmosphere on the Moon with similar surface density to Earth and that it would not reach up too high out of the Moon’s gravity well to be stable ,but it would have to mass 10^18 kg. The escape rate would be 60 kg / second, so that would be about 1.9*10^9 kg per year. so an atmosphere as massive as that, if it could be created somehow, would last for many millions of years, even tens or hundreds of millions potentially. (Note he also wrote this, Creation of an artificial lunar atmosphere but it’s behind a paywall for me)

So, a lunar atmosphere like Earth is not so impossible as you might think, it would at least last for a fair while before it loses it. It is possible enough to need a bit more study.

Nick Hoekzema, a scientist from the Max Plank institute suggests that a near future developed lunar industry mining lunar rocks for metals could easily produce 10^9 to 10^10 kilograms of oxygen a year. So could keep up with the loss from solar winds, indeed would continue to thicken the atmosphere. An Atmosphere for the Moon

Artist's impression of a terraformed Moon

Terraformed Moon by Exospace on deviantART

Here is a concept video of a terraformed Moon.

There are many problems to address. The surface is so dry, but also the rocks not at all hydrated, so if you added water as well, you’d get many chemical reactions with them. And it also has pure iron and other materials only partly oxidized. So it would absorb more oxygen than there is in the Earth’s atmosphere before it stabilized. If there was water, it would react with the rock creating an alkali ocean with a pH of about 10 or 11. And the reactions would cause the rocks to expand, causing probably strong quakes for thousands of years.

Also the current vacuum is a valuable asset. We might find the Moon is more valuable as a place close to Earth, easily accessible, with very high levels of vacuum readily available. Air Pollution on the Moon

On the other hand a tiny atmosphere on the Moon, e.g. produced by exploding 1% of the US arsenal of nuclear weapons, would be enough to stop micrometeorites, which might be an advantage. See this article by Nick Hoekzema a scientist from the Max Plank institute: An Atmosphere for the Moon

Then also, at least to start with, the Moon is of great scientific interest as is. Surely we want to explore the ice at its poles, the caves, etc in the current vacuum conditions first, just to see what’s there and how it works as it is now, also to study the preserved record of the solar system in the ice cores, which may go back billions of years and to study processes in the surface layers from solar wind etc.

But as we find out more about it maybe we’d decide it is okay to transform it?

Also, just to mention this, there’s the issue of - what if the future Moon loses technology? Again this could make a fun science fiction story - a half million years into the future Moon with no technology but intelligent creatures adapted biologically to less and less oxygen, but eventually, not able to prevent their eventual extinction.

Or, if it lasts for millions of years by continually replenishing the atmosphere, what happens on those longer timescales if eventually the civilization that created it loses technology?

I don’t know how likely it is on short timescales (more likely if there is time for new creatures to evolve e.g. intelligent but without hands). But something you’d need to think about if guiding our Moon it into a new future like that.

As an easier alternative, humans could live in caves, or domed cities or you could cover the entire lunar surface with a “greenhouse” - in segments to deal with major asteroid impacts on the Moon, called paraterraforming. This is something we could do right away, and would encounter some of the issues such as the effects of Earth atmosphere on the lunar soil and rocks, at an early stage in this way, as surely something you could deal with on such a small scale as a domed city or cave.

See for instance this artist’s concept image of a paraterraformed Phobos (much smaller moon of Mars): Paraterraformed Phobos

See also Can we terraform the moon? If yes, how difficult is it? Is it possible with the current technology, and what are the major challenges might we face while terraforming? (here on quora)

How Do We Terraform The Moon? - Universe Today

Can We Terraform the Moon? A Second Home, Next Door?

Gregory Benford’s A Terraformed Moon Would Be an Awful Lot Like Florida

Oh, and you might be interested in our facebook group:

Case for Moon for Humans - Open Ended with Planetary Protection at its Core

and my article Case For Moon - New Positive Future For Humans In Space - Open Ended With Planetary Protection At Its Heart