The indication "K." or KV refers to "Köchel (Verzeichnis)", i.e. the (more or less) chronological (i.e. by composition date) catalogue of Mozart's works by Ludwig von Köchel. Note that this catalogue has been ammended several times, leading to ambiguity over some KV numbers (see e.g. Symphony N° 25). A version of the Köchel catalogue can be found here (http://www.heartflyer.com/mozartsworks.htm)
The compositions of Mozart listed below are grouped thematically, i.e. by type of composition. Not all thematic groups of Mozarts works have a separate numbering that is generally accepted: Köchel only numbers Symphonies (1 to 41); Piano concertos (1 to 27, leaving out some early transcriptions by Mozart) and a few other groups, on the other hand, for string quartets, most chambre music and vocal music there is no such numbering (or at least no general accepted one).
Only relatively few of Mozart's compositions have Opus numbers, while not so many of his compositions were published during his lifetime (the Haydn string quartets Op. 10 as a notable exception), so numbering by Opus number proves quite unpractical for Mozart compositions.
Thematic list of Mozart compositions
This list gives some better known examples of Mozart's over 600 catalogued compositions.
As a child prodigy Mozart toured Europe and became widely regarded as a miracle of nature because of his musical gifts as a performer of piano, harpsichord, and organ and as a composer of instrumental and vocal music.
In 1767, at age 11, Mozart transformed piano sonatas by various composers into his first four piano concertos through the addition of interludes and episodes for orchestra.
During the last years of his life Mozart was plagued at times by financial difficulties, as revealed in a series of letters he wrote to his fellow Freemason Michael Puchberg, in which he begged for loans.
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