In the first book, Ged comes of age. In the second book, Tenar comes of age, in a manner determined largely by the actions of Ged. In this, the third book, Arren comes of age, also influenced by Ged. (Ged is also influenced by Tenar and Arren, but he had already achieved at least the beginning of adulthood in the first book.)
I shall give away more of the plot of this book than I usually do when discussing a book.
Le Guin has usually been concerned with non-human organisms, with the living community, although her books are mostly about people. Shore is no exception:
As well as illustrating Le Guin's concern for the living community, this passage introduces the Master mages of Roke, and their various magical abilities. (Ged is the Archmage, by this time.) The Master Patterner, in all three of the books, does not perform any magic. (Other mages, and mages in training, including Ged, do perform magical acts in the books.) The Master Patterner observes nature, and the deep patterns that underly existence in Earthsea -- the equilibrium of the world. He, and Ged, have decided that there is a serious problem with the way things are. (For a quotation on equilibrium, from this book, see here.)
Early in the book, Arren, a teenage boy from a noble family, comes to Roke Island, where the Master Mages live, as a messenger from his father, himself with some magical ability and training. The father wants to know what is wrong with the performance of magic -- why do the spells, the actions, seem to have lost their meaning. In a conference with the nine Master Mages, Ged decides that, in the first place, Arren has not come to Roke at this time by chance. In the second place, Ged decides that, if Arren is willing, he will take him on a journey, mostly in Ged's boat, the Lookfar, to find the source of the problem with the equilibrium. That problem, Ged is certain, is caused by a man.
Eventually, they do find the cause of the problem, and that cause is a man, a man with powerful magical abilities, and a man who fears death greatly, so greatly that he has developed spells that allow him to return to life, even after being killed. The existence of such spells acts as a tremendous attraction for the mages, and others with magical ability, of Earthsea. All those with magical ability are, at times, able to enter into the spirit world, and it is there that they somehow feel the existence of the possibility of escaping death. This possibility attracts most of them. But it has its cost. They are made aware that, in order to escape death, they must give up their magical ability, and their secret names. (Their secret names are kept secret because knowledge of such a name would make it possible for a person with magical power to control, kill, or injure, by use of the secret name.) Many of the people of Earthsea who have magical ability give it up, and give up their secret names. Ged will not. He sees death as a necessary consequence of life. Giving up the secret name, and the ability to perform magic, does not hold off death. The promises of Cob, the man who fears death so much, are false. Only Cob can come back from death. (Cob is a use-name, not a secret name. Cob, too, has given up his secret name, the name given to every child in Earthsea.)
One of the finest things about this book is the dragons. Le Guin's dragons are intelligent, long-lived, and dangerous. Ged and Arren are guided to Selidor, the westernmost of the islands of Earthsea, by a dragon, Orm Embar. The dragon does so because dragons, too, partly live in the spirit world, and their equilibrium, too, has been damaged.
On Selidor, Ged sees Cob. Orm Embar gives his life to kill Cob, and Ged takes Arren with him into the Dry Land, the spirit world of the dead, to follow Cob. After a long journey in the Dry Land, they come to a Dry River. That River, although it has no water, comes out of a hole in the rocks, into a dry stream bed. Ged exerts all his power of magic, and closes the hole, thus blocking Cob's access back to the world of the living.
Ged and Arren manage to walk all the way across the Dry Land, to the other side, and re-enter the world of the living. There Ged has no magical power, and not much life. A great dragon carries Ged and Arren back to the centers of power of Earthsea, Roke and Havnor, and then carries Ged, now no longer a mage, back to his original home on the island of Gont. (Several years after the publication of Shore, Le Guin wrote Tehanu, which is about Ged and Tenar on Gont. I have posted on that book here.)
There are several aspects of the story, having to do with religion, that deserve emphasis. Ged, and the dragon, Orm Embar, give up a lot to restore equilibrium. There seems to be some power, although it is not specified what it is, that determines events, such as Arren coming to Roke at the proper time. A god? Perhaps. Finally, the view of death put forth in Shore is remarkable. The dead all go into the Dry Land, and are there for eternity, apparently. While there, they have no emotions, no attraction to people who were very important to them in life, and, in fact, they have no life, just a monotonous existence. But Ged believes that life, once lived, is important. But not so important that it should continue on and on. Le Guin is a Taoist. I do not know if the view of death in Shore is hers, or Taoist. But it is not the view of Christianity, which believes that death leads, at least for believers, to eternal abundant life.
A powerful book, with good character sketching, fine writing, and dealing with the most important issue humans face -- death.
Thanks for reading.