Welcome to part one!
The opening of this arrangement is very homophonic in nature, using a variety of inversions in block chord format. Take for instance the opening bar. In its most basic form we actually have a c major chord accompanying the melody, however it would be quite boring and a little unexciting not to make use of various inversions at this point.
Rather than just one C chord we have the following:
Cmajor - C/B - Amin7 - C/E
Put simply, these chords are essentially C chords with an altered bass note. Doing this helps to add more colour and makes for a more interesting journey for the listener. As you play, be sure to bring out the soprano(highest) note in the chords as it makes up the melody, and be sure to pay close attention to the voice leading within the chords.