At the most basic level, a circle with a stroke (but no fill) and the trim paths animator will do the trick for the edge. Then it looks like they used an animated circle as a track matte for the main body of the logo. Create a circle that covers the entire inside of the logo, animate its scale from 0-100 and then animate its position from the bottom corner of the logo to dead center where it covers the whole thing. Place that on top of the main body logo layer and on the main body logo layer select Alpha Matte as the track matte. Those two things should get the animation for you.