New to Steam and library not playing along

[comda]

Greetings!

Im getting slightly annoyed because I am new to steam and what I can't seem to understand is I've added a few games to my "library" on steam, but each time I install steam on a new PC my library is empty. Should It not have the games that I already installed? For example. I have downloaded Trackmania nations forever, and when I search for it on the new Pc I just got up and running it says in the green box (in library) but before I install it my actual library from the top is empty. even the drop down says 0. So each time I go to my other PC I have to go back to the previous to research what free games I have installed and search for them. Is this normal?

[BC_Programmer]

Your Steam library tracks the games you've paid for; as a result, free games don't appear in your library when there is no local content for the game.

This was actually because there were a lot of complaints when, previously, all free games appeared in your library, as well as later when they changed it so that free games would appear in your library after you played them.

[comda]

BC_Programmer,

Thanks for the quick reply. Started to assume that was the case but was not able to confirm. So thank you i appreciate that.