What is the material on my garage?

[fjonsson1]

I have issues with moisture in the garage. Some drywall sheets are completely bad and need to be replaced. But of course, the root problem needs to be looked at, how the moisture is getting in. I guess it's because water collects and just sits there.
So my question is, what is there today?
Is it something that can be fixed in the seams or is it time to replace everything?

 

[Stefan N]

Should have installed a new roof with more slope, just need a little more so the water runs off. Simply sealing the joints will probably last for about fifteen minutes or so.