In Gran Soren, talk to Steffen, usually wandering about, around the fountain square and to the East. He has long searched for a certain tome: Salomet's Grimoire. Its pages hold the power to grant the reader command of grand arcane magicks. The book itself is ensorceled. Even a novice is a grand wizard with that grimoire in hand. He wants you to seek the grimoire out and bring it to him.

This begins the quest:

A Troublesome Tome
Learn More of the Grimoire

Objective
Steffen asks you to locate Salomet's grimoire, a tome empowered wit arcane magicks. It seems the book yet remains somewhere in Gransys

Talk to Camellia in Camellia's Apothecary nearby. She tells you that her Apothecary is an honest business. The magick tomes are often either forgeries or stolen properties. She suggest thieves are more likely to hold or know about such a grimore. This updates the quest:

A Troublesome Tome
Explore the Thieves' Den

Details
The grimoire is stored somewhere in the bandits' hideout. Search the area and claim the tome.

You will see two red markers on your map. First, go to the one in the south, near the road to the Encampment. You run across a wandering scholar called Rowland. He is under attack by some bandits, kill them and afterwards talk to Rowland. He says he had the book in his possession, but that thieves stole it from him.

Your quest log updates again:

A Troublesome Tome
Investigate the Thieves

Details
A band of thieves has apparently claimed the tome. Head for their territory in the south of Gransys.

Go to the Ruins of Aernst Castle. These ruins are located a little south west of Witchwood.

Note: There are two bandit camps you might encounter in this quest. The female bandit camp, led by Ophis, is in the Ruins of Heavenspeak Fort. You don't need anything from there for now. If you come across the female bandits, you are in the wrong place. Also, if you are a male character, Ophis won't give you any information unless you are wearing a set of lady's garb from the Black Cat. If you do, she directs you to the Rival Camp in Aernst Castle. The male bandit camp is in the Ruins of Aernst Castle. Do not kill the male bandits leader, Maul, as he is actually a quest giver for the quest "No Honor Among Thieves". You do not need to kill any bandits to get the Grimoire. It is best to avoid them altogether for now, if possible.

Location of Salomet's Grimoire
Enter the fort, climb the spiral stairs inside all the way to the top of the fort's tower. When you arrive at the top, it is not really the top. You need to climb on a ledge, and climb even further up. Loot the chest.

See picture below, taken from the top of the stairs, to help you figure out where to climb the wall.

Dragon's Dogma Grimoire Location

You find:

Salomet's Grimoire
A legendary tome of potent magick. Any may wield it, but only once ere the book crumbles.

After you have recovered it, deliver the Grimoire to Steffen. Hand it over, and this will complete the quest, A Troublesome Tome.