What's in a series, anyway? Most of us would agree that it's simply a linked set of books, but might vary wildly on how they might be linked. Most conventionally, they would be sequential, and follow similar characters through an elongated arc - like Lord of the Rings, or even Game of Thrones. Recently however, I've been finding that many of my favourites follow another model.
As you might have guessed, I'm about to talk about Bujold and Brust. A lot. Bujold's longest series is the Vorkosigan Saga, a set of books that mostly follows the Vorkosigan (and future Vorkosigan) family of Barrayar, a galactic backwater with some interesting quirks (it was colonised, cut off, then rediscovered after reinventing feudalism - then its new spacefaring neighbours tried to invade, leaving in their wake a rapidly modernising planet with an odd social structure and extreme taboos against mutation, the visible sign of the radiation weapons used in the war). It switches between a number of different protagonists - chiefly Miles, who I adore (you can read about my adoration for him plenty elsewhere, though pointing out that he is a disabled, brilliantly flawed man who doesn't escape his own consequences as well might give you some clues), but also Cordelia, his mother, and even one book with the amazingly lazy Ivan (usually suffixed with "you idiot"). But the freedom in not being bound to follow one particular plot arc between books means each acts fundamentally as a standalone - if changing character, genre, and setting needs to happen, then it can. Which makes for a far more varied read, while still preserving the advantages of a series: greater character depth, familiarity and development. By the latter books of the Saga, Miles is one of the best characters in modern fiction, with remarkable complexity - but if we'd had to read a similar number of books all structured as The Warrior's Apprentice, most of us would have stopped reading long ago. The freedom to retain worldbuilding and character while changing genre and plots gives it the best of both worlds.
Another author doing similar work is Steven Brust in his Vlad Taltos novels, following the life and times of the titular character. It takes similar freedoms to Bujold's Vorkosigan Saga, but with an additional one: chronology. The Vlad Taltos series is far looser chronologically than Bujold's - Vlad will mention a story as an anecdote in one book, then eventually tell it as its own story. The events of Taltos, the fourth book, are referred to in Jhereg, the very first. This is important in two further ways: firstly, it allows the series as a whole to start in media res - the Vlad Taltos series informs us where it is going with Jhereg, making the reader willing to tolerate more buildup in its beginning when eventually told - and secondly, it gives us a far firmer impression of Vlad-as-narrator. For first person stories, this is definitely an additional benefit: Vlad will allude to other stories, shared anecdotes, then tell them in other books altogether, making us believe far more in him as a character telling the story himself. Kvothe, while a good storyteller, rarely gives this impression - his story is far too well structured.
As you might have guessed, I'm about to talk about Bujold and Brust. A lot. Bujold's longest series is the Vorkosigan Saga, a set of books that mostly follows the Vorkosigan (and future Vorkosigan) family of Barrayar, a galactic backwater with some interesting quirks (it was colonised, cut off, then rediscovered after reinventing feudalism - then its new spacefaring neighbours tried to invade, leaving in their wake a rapidly modernising planet with an odd social structure and extreme taboos against mutation, the visible sign of the radiation weapons used in the war). It switches between a number of different protagonists - chiefly Miles, who I adore (you can read about my adoration for him plenty elsewhere, though pointing out that he is a disabled, brilliantly flawed man who doesn't escape his own consequences as well might give you some clues), but also Cordelia, his mother, and even one book with the amazingly lazy Ivan (usually suffixed with "you idiot"). But the freedom in not being bound to follow one particular plot arc between books means each acts fundamentally as a standalone - if changing character, genre, and setting needs to happen, then it can. Which makes for a far more varied read, while still preserving the advantages of a series: greater character depth, familiarity and development. By the latter books of the Saga, Miles is one of the best characters in modern fiction, with remarkable complexity - but if we'd had to read a similar number of books all structured as The Warrior's Apprentice, most of us would have stopped reading long ago. The freedom to retain worldbuilding and character while changing genre and plots gives it the best of both worlds.
Another author doing similar work is Steven Brust in his Vlad Taltos novels, following the life and times of the titular character. It takes similar freedoms to Bujold's Vorkosigan Saga, but with an additional one: chronology. The Vlad Taltos series is far looser chronologically than Bujold's - Vlad will mention a story as an anecdote in one book, then eventually tell it as its own story. The events of Taltos, the fourth book, are referred to in Jhereg, the very first. This is important in two further ways: firstly, it allows the series as a whole to start in media res - the Vlad Taltos series informs us where it is going with Jhereg, making the reader willing to tolerate more buildup in its beginning when eventually told - and secondly, it gives us a far firmer impression of Vlad-as-narrator. For first person stories, this is definitely an additional benefit: Vlad will allude to other stories, shared anecdotes, then tell them in other books altogether, making us believe far more in him as a character telling the story himself. Kvothe, while a good storyteller, rarely gives this impression - his story is far too well structured.