The drum groove on Peter Gabriel's "In Your Eyes", from the So album, is one of those grooves every drummer would like to learn to play.
The drum/percussion mix, like many Peter Gabriel tunes, is thick with lots of African influenced rhythms and percussion instruments. It's no surprise to see that two drummers, Jerry Marotta and Manu Katché, both playing drums on this song, with Manu also playing percussion and talking drum.
Here is the basic groove from the pre-chorus and chorus of the tune, as heard/seen in Peter Gabriel's live version of "In Your Eyes", which has one drummer, plus percussion.
In the verse, the drum groove is essentially just sixteenth-notes on the HiHat over the same Kick drum pattern as notated above. I've notated the Kick drum sixteenth-note 'push' before beat three in parenthesis because this is sometimes left out and covered by other percussion instruments.
The notation above outlines the drumkit #1 part of the pre-chorus. On the CD recording, there's no 'open' HiHat on beat 3, and the HiHat accents are only implied and subtle; live versions it's as written. Drumkit #1 in the chorus takes the same approach is in the pre-chorus. On the CD you can hear drumkit #2 playing a Mounted-Tom where you see the notated HiHat accents above (off-beat sixteenths). Knowing this, with the correct set-up and some creative sticking, you could theoretically cover much of what drumkit #1 and #2 are playing. But for this transcription, and what I suggest working on first, it's the basic pattern that I've notated above, knowing that percussion (live and/or programmed) will/can fill in the rest.
So there it is ... the basic groove to "In Your Eyes" ... enough to hopefully get you on your way, and leave you plenty of room to create and express yourself, just like Jerry and Manu did on the original recording.