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If you haven't seen the Intro to Animation Curves in After Effects tutorial yet, I recommend looking at that one first, as this one references some of the concepts in it.
Squash and Stretch is one of the main principals of animation, yet a lot of animators leave it out of their work. I'm going to show you the basics of this technique, and then show you how to apply it in After Effects. It will give you another tool to polish and finesse your animations, giving things more weight and oomph.