The verse is in E major, but he made the IV chord, (normally an A major chord), into a minor chord (A minor). It's an extremely common device.
Note that the melody that he sings on the A minor chord, you could indeed play the IV major chord (A major). You could also try some other "A chords as well; A7, A7sus4, A sus4. The technique is called "modal interchange". Other substitute chords you can try in that spot are D7, F#mi7b5, F major7, D minor9, Bb maj7b5 (those were worked out through the overtone series...check out my buddy Helmholtz). The bridge is a ii-V-I progression in the key of G major (Ami-D7-G). Eventually he throws in the E7 chord, which is a fifth above the following chord which starts the verse (A minor); so he's set up a "secondary dominant" into the Ami chord, a type of V7-i progression.