I have defined three main points on the line to describe book series.
First is the series that is really one big long book, broken into pieces. The Lord of the Rings is the best example of this type of story. It's one big arc, and the individual books don't make much sense by themselves. (A season of the TV show "24" is an example of a TV show like this.)
On the other end of the spectrum is the series of books where each book is a distinct story and separate from the others. The characters usually remain the same, and often the setting, but other than that each story can be picked up and read all by itself. The stories of Horatio Hornblower are like this. You can read one and it is a complete story, with only a little bit of back story to pick up along the way. I imagine the James Bond series is like this too. (Most TV shows are like this, especially sitcoms--with the occasional multi-episode to-be-continued show. The old "Star Trek" episodes are a classic example.)
In the middle of the continuum is the series of books where each book is a complete story, but also is part of a bigger story arc. These are rarer. The best example I can think of is the Harry Potter series. Each book as a particular plot, but the overal themes and threat of Voldemort are always there. (Many modern TV shows like "Buffy" or "Battlestar Galactica" are like this. The first Star Wars trilogy is a great example.)
Gene Wolfe's
The Book of the New Sun falls into the first type. It is a series of four books, which was republished as two books recently.
Shadow and Claw comprises the first two books of the series,
Shadow of the Torturer and
Claw of the Conciliator.
The book takes place in the distant future, when the sun is dying and humans await the coming of the New Sun. The story is about Severian, a member of the guild of torturers. He is assigned to help take care of a young woman named Thecla, a noblewoman imprisoned as leverage against her sister and the sister's lover, a rebel. Severian falls for Thecla, and when she is destined for torture and death, he gives her a dagger to take her own life. Now an outcast, he is sent to a city in the north to be an executioner.
Severian doesn't make it out of the city before he is challenged to a duel by an armored warrior. A woman named Agia helps him pick the flower for the duel, and they pull a woman named Dorcas out of a lake. He survives the duel, and his opponent turns out to be the brother of Agia, and they had conspired to kill him and take his sword, since he wouldn't sell it. He ends up executing Agia's brother, after the man is convicted of murdering innocent bystanders at the duel. Before leaving the city, Severian and Dorcas act in a play put on by a man Severian met a few days earlier. And Severian realizes that he is carrying the Claw of the Conciliator, an ancient relic which Agia stole and slipped into his bag.
The second book opens with Severian executing a woman in another city. He is nearly killed by Agia and her cronies. Separated from Dorcas and the players, he travels with his new friend Jonas to the House Absolute, the residence of the Autarch, the ruler of the empire. On the way they join the band of the rebel who is with Thecla's sister, and Severian takes part in a ritual to eat Thecla's flesh and take her memories. The rebel gives him a mission to complete at the House Absolute. Severian and Jonas are captured and taken to a large detention chamber in the House Absolute, but with the help of Thecla's memories he manages to escape with Jonas. Jonas finds a device that transports him far away, after Severian learns he is really a machine with a man's face.
Severian runs into a man while wandering through the huge house, and realizes that the man is not only the man he is supposed to meet but he is actually the Autarch himself. He later finds Dorcas and the other players on the grounds, and the put on the play for the nobles at the house. Later they are separated, and Dorcas and Severian end up witnessing a witch calling forth a dead man through time.
I enjoyed the story, and am enjoying the second book (or third and fourth books). Severian is a barely likeable character, being a torturer who has committed the offense of giving his "client" a painless death. Being a first person narrator makes it that much more intriguing. He grows with the story, and comes to have the personal mission of returning the Claw to its rightful owners. Gene Wolfe has a way of making an outlandish plot seem reasonable, like the way Agia keeps cropping up to find Severian, or how Severian keeps finding Dorcas.
The sense of reality is keen throughout the story, and it's almost like it really is translated from a future text, as Wolfe implies in the appendix. He uses arcane and made up words, links the complex parts of society. It really feels like the culture he is describing is really millions of years old, with ancient technology and long lost epochs. I'll give the book an A. I am really enjoying the strange plot and the futuristic setting.