A sequel is a literature, film, theatre, television, music or video game that continues the story of, or expands upon, some earlier work. In the common context of a narrative work of fiction, a sequel portrays events set in the same fictional universe as an earlier work, usually chronologically following the events of that work.
In many cases, the sequel continues elements of the original story, often with the same characters and settings. A sequel can lead to a series, in which key elements appear repeatedly. Although the difference between more than one sequel and a series is somewhat arbitrary, it is clear that some media franchises have enough sequels to become a series, whether originally planned as such or not.
Sequels are attractive to creators and to publishers because there is less risk involved in returning to a story with known popularity rather than developing new and untested characters and settings. Audiences are sometimes eager for more stories about popular characters or settings, making the production of sequels financially appealing.
In movies, sequels are common. There are many name formats for sequels. Sometimes, they either have unrelated titles or have a letter added on the end. More commonly, they have numbers at the end or have an added word on the end. It is also common for a sequel to have a variation of the original title or have a subtitle. In the 1930s, many musical sequels had the year included in the title. Sometimes sequels are released with different titles in different countries, because of the perceived brand recognition. There are several ways that subsequent works can be related to the chronology of the original. Various neologisms have been coined to describe them.
The most common approach is for the events of the second work to directly follow the events of the first, either picking up dangling plot threads or introducing a new conflict to drive the events of a second story. A sequel to the first sequel might be referred to as a third installment or threequel or second sequel.
A sequel that portrays events prior those of the original work is called a prequel.
Parallels are stories that run at the same point in time within the universe of the story. 
A story that takes place in between two already existing works is referred to as a "interquel".
A spiritual successor is a creative work that in terms of function resembles a previous work, but officially is not titled a continuation.
A companion piece is a creative work that is associated with and complementary to another work. While a companion piece does not necessarily take place within the same "universe" as the predecessor, it must follow on specific themes and ideas introduced in the original work. Its creator must also intentionally mean for viewers to see it alongside or within the same context as the earlier work.
A reboot is a retelling or new envisioning of a story. It is similar to a remake. It means that a franchise's continuity begins anew, and/or elements of the continuity may be significantly retconned to accommodate a continuation of the series.
When a work is set in either the same universe or one very similar to that of its predecessors, yet has very little if any narrative connection to its predecessors and can be appreciated on its own without a thorough understanding of the backstory, then the work can be referred to as a standalone sequel. Star Trek II: The Wrath of Khan is an example of a standalone sequel. 
A remake is a motion picture based on a film produced earlier. The term remake can refer to everything on the spectrum of reused material: both an allusion or a line-by-line change retake of a movie. However, the term generally pertains to a new version of an old film. A reproduced television series could also be called a remake. Works that are referred to as a "re-imagining" are often remakes that take the basic elements of the original work, but are otherwise very different in style and plot, while "re-adaptations" are new adaptations of existing source material and "re-interpretations" are very loose adaptations that bear very little resemblance to the original work.
In The Afterlife of a Character, David Brewer describes a reader's desire to "see more," or to know what happens next in a narrative after it has ended. This capacity for expansive curiosity is certainly not restricted to a particular era in human history. Indeed, we can point to Homer's Odyssey as a sequel to the Iliad in the sense that it expands upon plot and character elements established in the first text. That both the Odyssey and the Iliad were written in the 8th century B.C.E. and are traditionally held to represent the first extant works of western literature lends credence to the ubiquity of sequels in literary history. The Judeo-Christian Bible is also a common referent in that sense; many of the works included in the Hebrew Scriptures can be classified as sequels in that they continue and expand on a very general narrative that is pre-established by previous books in the same collection. In addition, the development of an official canon allows for the distinction between official and unofficial sequels; in this context, apocrypha might be considered an early form of informal sequel literature. Sequels, then, become an important facet of Western literature throughout history. The medieval genre of Romance, in particular, contains massive networks of prequel and sequel literature.
The substantial shift towards a rapidly growing print culture and the rise of the market system by the early 18th-century meant that an author's merit and livelihood became increasingly linked to the number of copies of a work he or she could sell. This shift from a text-based to an author-centered reading culture led to the "professionalization" of the author -- that is, the development of a "sense of identity based on a marketable skill and on supplying to a defined public a specialized service it was demanding". In one sense, then, sequels became a means to profit further from previous work that had already obtained some measure of commercial success. As the establishment of a readership became increasingly important to the economic viability of authorship, sequels offered a means to establish a recurring economic outlet.
In addition to serving economic profit, the sequel was also used as a method to strengthen an author's claim to his literary property. With weak copyright laws and unscrupulous booksellers willing to sell whatever they could, in some cases the only way to prove ownership of a text was to produce another like it. Sequels in this sense are rather limited in scope, as the authors are focused on producing "more of the same" to defend their "literary paternity". As is true throughout history, sequels to novels provided an opportunity for authors to interact with a readership. This became especially important in the economy of the 18th century novel, in which authors often maintained readership by drawing readers back with the promise of more of what they liked from the original. With sequels, therefore, came the implicit division of readers by authors into the categories of "desirable" and "undesirable"--that is, those that interpret the text in a way unsanctioned by the author. Only after having achieved a significant reader base would an author feel free to alienate or ignore the "undesirable" readers.
This concept of "undesirable" readers extends to unofficial sequels with the 18th century novel. While in certain historical contexts unofficial sequels were actually the norm (for an example, see Arthurian literature), with the emphasis on the author function that arises in conjunction with the novel many authors began to see these kinds of unauthorized extensions as being in direct conflict with authorial authority. In the matter of Don Quixote (an early novel, perhaps better classified as a satirical romance), for example, Cervantes disapproved of Alonso Fernández de Avellaneda's use of his characters in Second Volume of the Ingenious Gentleman Don Quixote of La Mancha, an unauthorized sequel. In response, Cervantes very firmly kills the protagonist at the end of the Second Part to discourage any more such creative liberties. Another example is Samuel Richardson, an 18th-century author who responded particularly strongly against the appropriation of his material by unauthorized third parties. Richardson was extremely vocal in his disapproval of the way the protagonist of his novel Pamela was repeatedly incorporated into unauthorized sequels featuring particularly lewd plots. The most famous of these is Henry Fielding's parody, entitled Shamela.
In To Renew Their Former Acquaintance: Print, Gender, and Some Eighteenth Century Sequels, Betty Schellenberg theorizes that whereas for male writers in the 18th century sequels often served as "models of paternity and property," for women writers these models were more likely to be seen as transgressive. Instead, the recurring readership created by sequels let female writers function within the model of "familiar acquaintances reunited to enjoy the mutual pleasures of conversation," and made their writing an "activity within a private, non-economic sphere." Ironically, through this created perception women writers were able to break into the economic sphere and "enhance their professional status" through authorship.
Dissociated from the motives of profit and therefore unrestrained by the need for continuity felt by male writers, Schellenberg argues that female-authored sequel fiction tended to have a much broader scope. He says that women writers showed an "innovative freedom" that male writers rejected to "protect their patrimony." For example, Sarah Fielding's Adventures of David Simple and its sequels Familiar Letters between the Principal Characters in David Simple and David Simple, Volume the Last are extremely innovative and cover almost the entire range of popular narrative styles of the 18th century.
In some cases, the characters or setting of an original film or video game become so valuable that they develop into a media franchise. Generally, a whole series of sequels is made, along with merchandising. Multiple sequels are often planned well in advance and actors and directors may sign extended contracts to ensure their participation. This can extend into a franchise's initial production's plot to provide story material to develop for sequels called sequel hooks.
Movie sequels do not always do as well at the box office as the original, but they tend to do better than non-sequels, according to a study in the July 2008 issue of the Journal of Business Research. The shorter the period between releases, the better the sequel does at the box office. Sequels also show a faster drop in weekly revenues relative to non-sequels.
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Sequels are most often produced in the same medium as the previous work (e.g. a film sequel is usually a sequel to another film). Producing sequels to a work in another medium has recently become common, especially when the new medium is less costly or time-consuming to produce.
A sequel to a popular but discontinued television series may be produced in another medium, thereby bypassing whatever factors led to the series cancellation.
Some highly popular movies and television series have inspired the production of multiple novel sequels, sometimes rivaling or even dwarfing the volume of works in the original medium.
For example, the 1956 novel The Hundred and One Dalmatians, its 1961 animated adaptation and that film's 1996 live-action remake each have a sequel unrelated to the other sequels: respectively The Starlight Barking (1967), 101 Dalmatians II: Patch's London Adventure (2003, direct to video) and 102 Dalmatians (2000).
Sometimes sequels are produced without the consent of the creator of the original work. These may be dubbed unofficial, informal, unauthorized, or illegitimate sequels. In some cases, the work is in the public domain, and there is no legal obstacle to producing sequels. An example would be a book or movie that served as a sequel to the original book The Wonderful Wizard of Oz, which is in the public domain (as opposed to the 1939 movie). In other cases, the original creator or their heirs may assert copyrights and challenge the creators of the sequels.
Another example of an unofficial sequel would be Never Say Never Again, a James Bond movie starring Sean Connery that was not produced by Eon Productions, which has handled nearly all of the other Bond films.
Prequels focus on the action that took place before the original narrative. For instance, in Star Wars: Episode III - Revenge of the Sith the audience learns about how Darth Vader originally became a villain. A prequel assumes that the audience is familiar with the original--the audience must rework the narrative so that they can understand how the prequel leads up to the beginning of the original.
Of particular interest to me in this essay is the shift from a text-based to an author-based culture, accompanied by a developing elevation of the original author over the imitative one.