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.
Symphonies
Symphony No. 25 in G minor, K. 183 (173d B)
Symphony No. 35 "Haffner" in D major, K. 385
Symphony No. 36 "Linz" in C major, K. 425
Symphony No. 38 "Prague" in D major, K. 504
Symphony No. 39 in E flat major, K. 543
Symphony No. 40 in G minor, K. 550
Symphony No. 41 "Jupiter" in C major, K. 551
Concertos
Bassoon Concerto in B flat major, K. 191
Oboe Concerto in C major, K. 314
Concerto for Clarinet and Orchestra in A major, K. 622
Piano Concerto No. 17 in G major, K. 453
Piano Concerto No. 19 in F major, K. 459
Piano Concerto No. 20 in D minor, K. 466
Piano Concerto No. 21 in C major, K. 467
Piano Concerto No. 23 in A major, K. 488
Piano Concerto No. 24 in C minor, K. 491
Piano Concerto No. 25 in C major, K. 503
Piano Concerto No. 26 "Coronation" in D major, K. 537
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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