The Minmatar Republic is rather young
Note that the name of the people is not "Minmatar" but "Matari" named after their home planet Matari. Though minmatar is more commonly used.
The people of Minmatar Republic originate from planet Matar. The people of Matar were enslaved by the Amarr Empire around one thousand years ago starting in 881 BYC. It was until 20 BYC when the opportunity for Minmatar rebellion came when the Amarr Empire lost the Amarr-Jove war. Even to this day half of Minmatar live under Amarr control.
Among the Minmatar there are seven tribes: Sebiestor, Brutor, Krusual, Vherokior, Starkmanir, Thukker Tribe and Nefantar. Though only five of these are part of the Minmatar Republic. The thukker have their own independent nation and Nefantar are part of Amarr empire under the name Ammatar Mandate.
Minmatar in PvE
The Minmatar rats deal mostly explosive and kinetic damage with heavy emphasis on explosive damage, though it is not uncommon for some Minmatar ships to also deal EM or thermal damage. The Minmatar ships are weakest against explosive damage with kinetic being second best damage to use.
The EWAR of choice for Minmatar rats is target painting. The effect of this is small so it can be mostly ignored.
The Minmatar Republic offers full set of ships from shuttle to titan. The Minmatar ships are known for their superior speed and equipped with mostly projectile turrets though several missile ships also exist. The Minmatar ships are versatile and are most able to use both shield and armor tank.
The Republic Fleet also offers several upgraded navy faction hulls for capsuleer use.