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The term kawthar is an intensive form of the noun kathrah (Zamakhshari), which, in its turn, denotes "copiousness", "multitude" or "abundance"; it also occurs as an adjective with the same connotation (Qamus, Lisan al-'Arab, etc.). In the above context, which is the sole instance of its use in the Qur'an, al-kawthar obviously relates to the abundant bestowal on the Prophet of all that is good in an abstract, spiritual sense, like revelation, knowledge, wisdom, the doing of good works, and dignity in this world and in the hereafter (Razi); with reference to the believers in general, it evidently signifies the ability to acquire knowledge, to do good works, to be kind towards all living beings, and thus to attain to inner peace and dignity.
This includes a heavenly river as well other favours in both worlds.
Al-Kauthar literally means "good in abundance". It is the abundant bounty which Allah bestowed on Prophet Muhammad (peace be on him). This includes a river (or fountain) in heaven of this name which Allah has promised the Prophet (peace be on him).