Terraforming Mars is a big job. The way to do it is to go to Saturn's rings and redirect tens of thousands of frozen gas icebergs to slam into Mars. It would be best to get started on that before too many people move to Mars.

Sweet... but how about cleaning up the current mess we have made of te rock we are on, right now!

you mean frozen water icebergs? they can split the water to make oxygen.

Maybe we can use methods of splitting CO2 on Earth to stop global warming.

Why not do a "Star Trek" move and send a probe to inject bacteria into the Mars atmosphere? A bacteria that multiplies and thrives in the thin Martian air and eventually creates the needed atmosphere suitable for earthlings. It might prove cheaper and faster than hauling machinery to Mars to Terra- form the atmosphere...

These are interesting ideas, but what about using plants in constructed greenhouse biospheres? Mars' air, which is rich in CO2, could be pumped into the biospheres, and oxygen generated from the plants would then be pumped out to the human-habitable areas of the constructed dwellings.
Excess CO2 from the human-habitable areas could be pumped back into the biospheres. Any excess oxygen could be pumped into Mars' atmosphere, which would result in a gradual change of the atmospheric composition.

@Ed Wapole - Who said anything about terraforming? This projects sole purpose is to leverage in situ resources to produce life support for human colonization. Terraforming is a multi-generational project that will require space capability we are nowhere near accomplishing in the next 15-20 years.
I like the Cyano Knights approach to using cyanobacteria. If they use the spirulina genus it will also produce food as spirulina is edible with minimal processing. So essentially the the machines collect available water, put it in pressurized photo-bio-reactors, colonists feed the tanks with poop, and CO2 gets bubbled through. The colony then gets oxygen and food.

I like the Cyano approach, too. Besides all the advantages cited by VirtualGathis, it avoids adding carbon monoxide to the atmosphere.

I still do not understand why we are skipping the Moon. Cold fusion is already on the brink of being developed. The moon is the place to go for abundant H3. It's also obviously less hostile than mars, and much closer. Makes zero sense to me.

what is the use of having breathable air if one cannot have exposed skin due to UV radiation? one has to be protected by a space suit in any case.