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That looks like a really nice gift, I'm envious.It looks to me like the outside graduations are for your azimuth.The semi-circle inside that is Percent of Slope which would be used in conjunction with the vial level.The interior semi-circle is Degree of Slope, also used with the vial level.You will notice that 100% is equal to 45° of slope.These two features are referrred to a (in)clinometers or a sort of Abny Level.They are used by flipping the compass on edge vertically and finding the proper site plane.The Bulls-Eye bubble is to assist in holding the compass level in order to obtain an accurate azimuth reading.The little button on the rim looks like a dampening mechanism to settle the needleA good Orienteering book will greatly assist you.I have used a compass for years and to this day, rarely find a need for GPS.Bring a map and use the two often and you will never get lost.Have fun and good luck!!Rob.
Anymore the hardest part of using a compass is acquiring a good map!
REI has a orienteering class that will teach you how to use a compass. Lots of hands on learning, I highly recommend it.https://www.rei.com/events/a/navigation
I highly recommend this book, although there are probably plenty of free videos or other electronic resources out there.https://www.amazon.com/Wilderness-Navigation-Finding-Altimeter-Mountaineers/dp/0898869536Covers declination, orienting, taking and following a bearing, triangulation IIRC, and more.
If you're going to use this for navigation in the woods, look up "magnetic declination". In WA, it will throw you're compass off 15 degrees or better. On a 2 mile hike, you'll miss you're target by over a half mile. That is really cool though. I would cherish that until I died.