A fugue is a fairly strict form of music composition; though it's loosened a bit over time, the most traditional examples of the form are very rigid. A fugue involves a variety of contrapuntal melodies, or parts, that work independently of each other until coming together near the end. It's somewhat like a canon; a fugue shares the same essential elements of counterpoint and shadowing.
A fugue usually has a bare minimum of three individual sections. The first section introduces the melodic theme, or subject, of the fugue in one part. Another part then mimics this theme but with certain variations; this following part can be a set interval above or below the leader or can even be in another key. The fugue melody then shifts to a third voice, which mimics the second; at this point, the first part will sometimes introduce a counterpoint while the second part is being shadowed. This chain of introduction and shadowing continues until every part has addressed the main subject.
The second part of a fugue develops the melody introduced in the first part but with a few crucial changes; these changes can be based on any of the melody's elements provided that it still retains an essential relation to the original subject. This contrapuntal element is given time to develop, moving through the various parts of the fugue at fixed points in time.
The ending of a fugue is usually a return to the original subject melody and its counterpoints. The rules are the most lax at this point in the fugue; the melodies can be repeated in the same or different order and can even incorporate canon-like rounds.
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