I’m new on this, so please be patient with me… I’ve already tried to install Unity, after running on Mate, but it seems that i’ve not the necessary files available on the repository or hard disk!
So, how can i set-up Unity? 
The easiest way is to download the ubuntu .iso and install plain Ubuntu 
or just try
sudo apt-get install ubuntu-desktop^
Do not forget the ^ at the end 
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Hi
If you're talking about the desktop environment that comes with standard Ubuntu, you can try:
sudo apt install ubuntu-desktop
Then at the login screen, you may be able to choose unity as an option.
I'm not sure at all this will work, if it doesn't you can also download the standard Ubuntu iso and do a fresh install using that.
Cheers
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I think that the following terminal command (Ctrl + Alt + t) should install the base unity packages on top of Ubuntu Mate?:
sudo apt-get install unity
As @wolfman and @ouroumov said, but you need the ^ at the end, so it will install all dependencies.
So the full sequence to do is
sudo apt-get update
sudo apt-get install ubuntu-desktop^
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@Paulo_Ramos I did the exact opposite - had straight up Ubuntu 16.04 installed and added the MATE desktop. This wasn’t a good idea for me. Subsequently on 2 different machines I installed Ubuntu MATE 16.04 and found these 2 installations more to my liking.
There’s absolutely nothing wrong with either distro however I don’t advise mixing the desktop environments and supplied applications.
IMO the best action for you is to download and install Ubuntu 16.04