It would be nice if there were an atmosphere on the Moon with oxygen; in fact it could be just oxygen at 1/5 the Earth's pressure. People could live there. Now of course given the Moon's lower gravity the atmosphere would escape into space, but it'd take hundreds of thousands of years for that (roughly 1 million years if I recollect well). Enough time for 50 human civilizations to develop one after another.
Now there is oxygen on the Moon, but it is fixed in rocks and probably in some water. What would be the best, easiest way to make an atmosphere out of it?
My guess is that can be done with a powerful enough energy source. Rocks or water can be decomposed by heating.
Using the Sun's light for that could do, if it is concentrated. Nuclear reactors and nuclear bombs could be used too, but that doesn't seem that easy because it costs to send them; making an automated nuclear plant / bomb factory on the Moon may be cheaper, but other problems appear (ores, plant defects etc.)
So my first guess to a solution would be using solar energy, with mirrors that can be built in place or brought from Earth (as thin sheets of plastic). But how much of the Moon's surface would have to be used? I wouldn't cover too much of it with oxygen factories; that would cost a lot too. Let's say we want an atmosphere there in a reasonable time (hundreds of years). What approach to use?