Short answers, pulled from the story.
A canon is a contrapuntal compositional technique in which a melody, called the leader or dux, is imitated by one or more additional voices, called followers or comes, entering after a set delay. The follower replicates the leader's rhythms and intervals exactly, or transforms them according to a set rule.
A round is a specific type of canon in which all voices are musically identical and the piece can repeat indefinitely. Canons broadly include many other forms, such as inversion canons, retrograde canons, and mensuration canons, where the follower may move backward, in contrary motion, or at a different speed than the leader.
The best-known early canon is "Sumer is icumen in", composed around 1250 and designated a rota, meaning wheel, in its manuscript source. Walter Odington gave the broader English round form the name rondellus at the beginning of the 14th century.
In the first act of Fidelio, four characters sing a quartet in canon, each delivering their own words to the same music. Antony Hopkins described the effect as inducing a trance that carries the protagonists outside time, with the softly padding gait and dove-tailed perfection of the counterpoint creating what he called a sublime musical wonder.
A mensuration canon has the follower imitate the leader at a different rhythmic speed, either doubling or halving the note values. Johannes Ockeghem wrote an entire mass, the Missa prolationum, in which each section is a mensuration canon at different speeds and entry intervals. Arvo Pärt used the form in Cantus in Memoriam Benjamin Britten, Arbos, and Festina Lente.
A puzzle canon, also called a riddle or enigma canon, is a canon in which only one voice is written out and performers must deduce the remaining parts and their entry points from clues. The earliest known example is an anonymous ballade, "En la maison Dedalus", found in the Berkeley Manuscript from the third quarter of the 14th century. J. S. Bach presented many of his canons in this form, including in The Musical Offering.