Hello to all of you,
I am new in the "After Effects world" and so far I can say that this is great, but still I have some questions and the most important question for the moment for me is:
"For example, I have a shape and when I click on the layer shape, the canvas points appear around that shape. What I want to do ... is to animate just the right side of that shape and the left side of the shape to stay fixed.
Below you can see an url link with a drawing of mine to explain you better what I want to do:
Is it this possible?"
Create a rectangular mask/ shape path and select the path points rather than a parametric rectangle.
As someone new to AE, I would highly recommend going through these resources: Getting started with After Effects
It will help you get a grasp on many things to do with using AE (including the question you asked, but Mylenium already answered that for you).