Nadsat is a fictional register or argot used by the teenagers in Anthony Burgess's novel A Clockwork Orange. In addition to being a novelist, Burgess was a linguist and he used this background to depict his characters as speaking a form of Russian-influenced English. The name itself comes from the Russian suffix equivalent of "-teen" as in "thirteen" (-надцать, -nad·tsat'). Nadsat was also used in Stanley Kubrick's film adaptation of the book.
Nadsat is a mode of speech used by the nadsat, members of the teen subculture in the novel A Clockwork Orange. The antihero and narrator of the book, Alex, uses it in first-person style to relate the story to the reader. He also uses it to communicate with other characters in the novel, such as his droogs, parents, victims, and any authority-figures with whom he comes in contact. As with many speakers of non-standard varieties of English, Alex is capable of speaking standard English when he wants to. It is not a written language: the sense that readers get is of a transcription of vernacular speech.
Nadsat is basically English with some borrowed words from Russian. It also contains influences from Cockney rhyming slang, the King James Bible, the German language, some words of unclear origin, and some that Burgess invented. The word nadsat is the suffix of Russian numerals from 11 to 19 (-надцать). The suffix is an almost exact linguistic parallel to the English '-teen,' and is derived from "на", meaning "on" and a shortened form of "десять", the number ten. "Droog" is Russian друг "close friend". Some of the words are also almost childish English such as eggiweg ("egg") and appy polly loggy ("apology"), as well as regular English slang sod and snuff it. The word like and the expression the old are often used as fillers or discourse markers. (Source: Wikipedia)
One of the most innovative aspects of A Clockwork Orange is the language Burgess’s protagonists employ. Nadsat, Russian for ‘teen’, is the invented slang in which Alex narrates the novel, his experiences described in raucous and unfamiliar prose. Much of his inspiration came from a holiday to Leningrad in 1961, which he discovered reminded him of the Manchester of his youth. It was a rare occurrence for a British citizen to travel to Russia in the 1960s at the height of the Cold War, and this is perhaps one of the reasons Burgess is often confused with spies of the period such as Anthony Blunt and Guy Burgess. Yet, the impetus for Burgess’s trip was cultural curiosity, and he hoped to produce a novel from his experience. In fact he produced two: A Clockwork Orange and Honey for the Bears (1963). Arguably, Tremor of Intent (1966) also contains some inspiration from this period. (Read more here.)