Although the tabla is probably only a few hundred years old, the music of tabla goes back several thousand years to the Vedic period. It is a modern vehicle for the expression of ancient music... . According to one theory, the tabla was invented in the 13th century by Amir Kushru (to whom some attribute the invention of the sitar), who is supposed to have divided a Mridanga into two separate pieces. This explanation is unlikely, however, because there are temple carvings of double hand drums resembling tabla that date back to 500 BC.
"Notwithstanding disputes regarding the origin of tabla, there is no controversy regarding Sidhar Khan (or Sudhar Khan) of Dheli as the first exponent of tabla playing. A contemporary of Sadarang, he lived in the 18th century. Sidhar Khan is also believed by some to have invented the tabla. In any case, it is known that he established the first style of tabla playing, know as the Dheli style, from which all others, except that of Punjab, originate."
[Aloke Dutta: Tabla lessons and practice, 1995,1].
Read a description of the Tabla.