For space travel: would you need to recreate earths air composition? Or could you just get by with the top 2 or 3 main components, i.e. either 78% nitrogen and 22% oxygen, or 78% nitrogen, 21% oxygen and 1% carbon dioxide?
In principle it is sufficient to ensure the partial pressure of Oxygen we have at sea level on Earth. Therefore roughly 0.2 atm of O2 would be enough.
Further dilution in inert gases like Nitrogen is preferred to prevent risks related to a pure oxygen atmosphere, but again what matters is the Oxygen partial pressure. So one could also live with a 0.7 atm pressure, given by 0.5 atm N2 and 0.2 atm O2.
There's a wide range of potential atmospheres that could be used.
The ISS uses a mix of oxygen and nitrogen at around 1 atmosphere (14 psi), recreating the air at sea level reasonably well.
The Apollo program flights used pure oxygen to save weight, at much lower pressure than a standard atmosphere (5 psi).
Anything between those extremes would work just fine. You could also mix in other inert gases, like argon or krypton, if you had the need, though you'd have to be careful.
Which option you choose depends on a lot of factors. If you have powerful engines and aren't too worried about weight, re-creating Earth's atmosphere would be ideal, since the nitrogen dilution reduces flammability. If you're trying to save weight, pure oxygen will do, but you need to be worried about fire.
You basically need oxygen to breathe. Everything else is not strictly necessary. The limits you are willing to take depend on how much of a mountaineer and how much of a diver you are.
These two articles explain the upper and lower limits for oxygen partial pressure for humans: https://en.wikipedia.org/wiki/High-altitude_adaptation_in_humans https://en.wikipedia.org/wiki/Maximum_operating_depth
Where the Tibetan highlanders live, the oxygen level is only about 60% of that at sea level. Most people will tolerate this level as a minimum, so you will have ~100mbar/10kpa of pure oxygen as a "minimum atmosphere". Breathing pure oxygen works well, as every tech diver will tell you. Still, everything that's not wet or otherwise inflammable will burn VERY easily, so that's why this is not a great atmosphere for space travel. Put something in to dilute it - like Nitrogen or Argon e.g.