The indication "K." or "KV" refers to "Köchel Verzeichnis", i.e. the (more or less) chronological (i.e. by composition date) catalog of Mozart's works by Ludwig von Köchel. Note that this catalog has been amended several times, leading to ambiguity over some KV numbers (see e.g. Symphony No. 25).
The compositions of Mozart listed below are grouped thematically, i.e. by type of composition. Not all thematic groups of Mozart's 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 most chamber music and vocal music there is no such numbering (or at least no generally accepted one).
Only relatively few of Mozart's compositions have opus numbers, as not so many of his compositions were published during his......