The "Geology for Beginners" Stranger mission in Red Dead Redemption 2 is available right from the start of Chapter 2 and can be completed at any time. It involves searching for 10 different Stone Carvings found in different areas of the map. As none are located in the southern part of the map, it's possible to complete this mission before reaching the Epilogue.
Please note that the Rewards section includes some heavy spoilers on the mission's ending, so refrain from reading it in full if you have yet to complete the quest and don't want any surprises to be spoiled.
The "Geology for Beginners" Stranger mission is given out by Francis Sinclair, a mysterious man living in a cabin found near Strawberry. The mission can be initiated at any time from Chapter 2 onward by just reaching his cabin, which can be found to the northwest of Strawberry, to the north of the "S" in Strawberry on the map, a little before the second road to the north of the "S" on the map. There's a mission that brings you to the area, so there's the chance that you won't even have to look for the cabin.
By speaking with Francis Sinclair, Arthur will learn of his quest of finding 10 different Rock Carvings, promising the outlaw a reward for mailing him the location of all ten. Accepting the task will begin the mission.
You can find all the locations below. We will cover them from west to east so that the journey to locate all of the carvings can be a little easier.
Rock Carving 1
The first Rock Carving is found in the West Elizabeth area. It's on the southwestern shore of the Owanjila lake, which can be found directly to the west of Strawberry. Ride along the shore and you will eventually find the carving on a relatively tall rock formation.
Rock Carving 2
The second Rock Carving in the West Elizabeth region is found right to the left of the first "T" in West Elizabeth on the map. The carving is actually located on top of Mount Shann. To reach it, you need to ride north of Strawberry and follow the path. Once near the top, you will find the carving.
Rock Carving 3
The third Rock Carving is the first of three found in the Ambarino region. It's located to the north of the second "Z" of Grizzlies West on the map. The actual carving is found near the peak of Mount Hagen. To reach it, you can use the O'Driscolls camp seen in Chapter 1 as a landmark to guide you. Just follow the trail past the camp to reach the peak and find the carving.
Rock Carving 4
The fourth Rock Carving and the second found in the Ambarino region is located near the Whinyard Strait, to the south of the gap between the "B" and second "A" in Ambarino on the map. The carving can be found on the west shore of the strait, very close to its northern end. The carving is right above to the right.
Rock Carving 5
The fifth Rock Carving, and the third and final one found in the Ambarino region, is located to the south of Moonstone Pond, a little to the north of the closest train track. The right spot is to the north of the "N" in New Hanover on the map. The right place can be easily recognized by a small rock formation. The carving is on the face looking north of one of the rocks.
Rock Carving 6
The last rock carving brought us closer to the New Hanover region, and that's where the final five carvings are located. The first one of this group is located to the north of Fort Wallace, right to the east of Bacchus Station. Following the shore of the Dakota River from Fort Wallace is a good way to get close to a mountain. Climb as far as you can and then spot a passage between the threes which will lead you to the top. The carving is found very close to the top.
Rock Carving 7
The seventh Rock Carving and the second found in the New Hanover region is found close to the Elysian Pool, to the north of the gap between the "E" and "R" in New Hanover on the map. On the eastern side of the pool, very close to the point where the Dakota River continues to the south, there a huge rock with the carving, which is visible from some distance.
Rock Carving 8
This Rock Carving, the third found in the New Hanover region, is found to the west of the "N" in Roanoke Ridge. Head to the area to see a rock formation rising from the plateau, the carving is facing the nearest road.
Rock Carving 9
The fourth Rock Carving found in the New Hanover region is located near the Elysian Pool. From the eastern side of the pool, you can reach a bridge. To the northwest of the bridge, there's a rocky area, and the carving is right on the top of the area.
Rock Carving 10
The final Rock Carving is one of the easiest to spot. To the northwest of Annesburg, near the Roanoke Valley, there's a place marked as Deer Cottage. Follow the path to the Cottage from the west and south and you should notice some rocks platforms. The carving is on the lower of the two platforms.
Simply finding the locations of the 10 Rock Carvings isn't enough to complete the mission, as you will have to mail Francis the exact location. To do so, just head into any Post Office and talk with the clerk at the counter.
Sending the first set of locations (i.e. any single set of co-ordinates) rewards players with a bottle of Kentucky Bourbon and $10. Sending the entire first set (i.e. first five) of coordinates rewards players with a Rock Statue. Sending the final set reveals a new letter from Francis, who asks Arthur to get back to his cabin new Strawberry.
Once inside the cabin, Arthur will understand the true nature of Francis by checking out his notes and drawings. Apparently, Francis is a time traveler from the future, and the rock carvings he asked Arthur to find depict objects found in cities like skyscrapers and the like. The drawings on the cabin also show how he and his people travel through time.
Francis being from the future also gives new meaning to his strange appearance. His birthmark is likely related to the fact that he may a descent of Kraff, a god worshipped by the Epsilon Program, a fictitious religious cult that has appeared in several Grand Theft Auto games.
Going back to Francis' cabin also allows players to get the real final rewards for the "Geology for Beginners" mission, the Old Brass Compass. The item can be brought to a fence, where it can be sold in exchange for the Raven Claw Talisman artifact. The artifact slows down weapon degradation by 20%.
Once out of Francis' cabin, the mission is finally complete.