As most of us I do not like to have many applications up at the same time. Not that I don't, but it could be more. So, when Adobe stopped to support AIR on Linux it was a bummer. I like TweetDeck and I was not about to install gazillion other apps just to be able to connect to the same.
Enter Wine. Wine is a compatibility layer capable of running Windows applications on several POSIX-compliant operating systems. So now I am back in business.
To get wine you simply install it from your repository like:
sudo yum install wine
sudo apt-get install wine
Then download TweetDeck for Windows (MSI version).
When you are finished to download the msi-file type the following in the command-line:
wine msiexec /i TweetDeck.msi
There you go. Running TweetDeck on Linux without Adobe AIR.