Absolutely..this is exactly one area After effects excels at. 2D motion graphics
Yes After Effects is designed to create such transitions as showed in the Video.
Please go through tutorial links on how you can create transitions and basic animation :
The above mentioned link has all the Learning essentials and Key techniques.
Thank you both for the answers. I tend to be a bit impatient and like to just jump right into things, but I know that instead of rushing and being so cavalier, I should actually learn the basics of the program first. I'm excited to begin learning this style of animating to make my videos more interesting. Thank you again, I appreciate the replies.