ActionBarActivity: cannot be resolved to a type

I am new to android-programming. I am following this tutorial to add an ActionBar to my Main_Activity using the explanation in the "Support Android 2.1 and Above" section.

I followed this tutorial to add a Library-Project. Then after adding the library, at the point "Add the library to your application project: I felt lost .. basically because I don't have the "add" option by itself in my Eclipse ..

however I clicked on "add library" and moved on ..

now when I change

to :

public class MainActivity extends ActionBarActivity { ... }

in my mainActivity.java , it gives me error (a red line bellow the ActionBarActivity and all methods' names and some functions) .. and again when i change:

<activity android:theme="@style/Theme.AppCompat.Light" ... >

in the Manifest, it also give me an error saying: No resource found that matches the given name ..

I am totally lost .. what did I do wrong ?