The name “bouzouki” comes from the Turkish word “bozuk”, meaning “broken” and comes from a particular reentrant tuning called “bozuk düzen”, which similarly used on its Turkish counterpart, the “saz-bozuk”.
It is in the same instrumental family as the lute. The body was carved from a solid block of wood, similar to the saz, but from its arrival in Greece in the early 1910′s it was modified by the addition of a staved back borrowed from the Neapolitan mandola, and the top angled in the manner of a Neapolitan mandolins so as to increase the strength of the body to withstand thicker steel strings.
The instrument which used in Rembetika music was a three-stringed instrument, but in the 1950′s a four-string variety was introduced.
The Greek bouzouki is a plucked musical instrument of the lute family, called the thabouras or tambouras family. The tambouras has existed in ancient Greece, and can be found in various sizes, shapes, depths of body, lengths of neck and number of strings.
The bouzouki and the baglamas are descendants of tabouras. The Greek marble relief, known as the Mantineia Base (now exhibited at the National Archeological Museum of Athens), dating from 330-320 BC, shows a muse playing a variant of the pandoura. From Byzantine era it was called pandouras and then tambouras. On display in the  National Historical Museum of Greece is the tambouras of a hero from the Greek revolution of 1821 one Greek general, Makriyiannis.
Other sizes have appeared and include the Greek instrument tzouras, an instrument smaller than the standard bouzouki. The 1919-1922 war in Asia Minor and the exchange of populations between Greece and Turkey, the ethnic Greeks fled to Greece. The early bouzoukia were mostly three-string (trichordo), with three courses (six strings in three pairs) and were tuned in different ways, as to the scale one wanted to play. At the end of the 1950s, four-course (tetrachordo) bouzoukia started to gain popularity. The four-course bouzouki was made popular by Manolis Chiotis who also used a tuning akin to standard guitar tuning, which made it easier for guitarists to play bouzouki, even as it angered purits. The first recording was made in 1958. The Irish bouzouki, with four courses, differently tuned from the Greek bouzouki, is a more recent development, stemming from the introduction of the Greek instrument into Irish music by Johnny Moynihan around 1965, and its subsequent adoption by Andy Irvine, Alec Finn, Dónal Lunny, and many others.

Bouzouki with four courses (tetrachordo)

Bouzouki with three courses (trichordo)