Allah (swt), may He be Blessed and Exalted, has told us that rivers flow from beneath Paradise: “And give glad tidings to those who believe and do righteous good deeds, that for them will be Gardens under which rivers flow….” [Al-Baqarah 2:25]
“For them will be Gardens of Eternity: beneath them rivers will flow….” [Al-Kahf 18:31]
The Prophet (saw) told us clearly about the rivers of Paradise. He said that during his Israa’ (Night Journey): “…I saw four rivers flowing out from beneath Sidrat al-Muntahaa, two visible and two hidden. He asked, “O Jibreel, What are these rivers?” He said, “The two hidden rivers are rivers of Paradise, and the two visible rivers are the Nile and the Euphrates”. [Muslim & Bukhaari]
Muslim reports from Abu Hurayrah that the Messenger of Allah (saw) said, “Sihran, Jihran, the Euphrates and the Nile are all from the rivers of Paradise”. [Sahih Muslim, Kitaab al-Jannah]
Sheikh Naasir ud-Deen al-Albaani said, “Perhaps what is meant is that these rivers originated in Paradise just as mankind did; this hadith does not contradict the well-established fact that these rivers spring forth from known sources on earth. If this is not in fact the meaning of this hadith, then it is one of the matters of al-Ghayb [the Unseen], which we must believe and accept because the Prophet (saw) has told us about it”. [Silsilat al-Hadith as-Saheehah, 1/18]
Another of the rivers of Paradise is al-Kawthar, which Allah has given to His Messenger (saw): “Verily We have granted you [O Muhammad] al-Kawthar [a river in Paradise]“ [Al-Kauthar 108:1]
The Prophet (saw) saw it and told us about it. Bukhaari reported from Anas ibn Maalik that the Prophet (saw) said,”Whilst I was walking in Paradise I saw a river whose banks were domes of hollow pearls, and I asked, “What is this, O Jibreel?” He said, “This is al-Kawthar which your Rabb has given to you”. And its scent – or its mud – was of fragrant musk”. Hudbah [one of the narrators] was not sure if he said tib [scent] or teen [mud]. [Sahih al-Bukhaari, Kitaab ar-Riqaaq]
Ibn ‘Abbaas explained, “al-Kawthar means the abundant blessings which Allah has bestowed upon His Messenger (saw).”
Ibn Katheer compiled a number of hadith [an-Nihaayah, 2/246] in which the Prophet (saw) spoke about al-Kawthar, such as the Narrated by Muslim from Anas, which states that when the aayah “Verily We have granted you al-Kawthar”  was revealed, the Prophet (saw) said, “Do you know what al-Kawthar is?” They said, “Allah and His Messenger know best”. He said, “It is a river that Allah (swt) has promised me and in it is much goodness”.
Another hadith narrated by Ahmad from Anas, according to which the Prophet (Saw) said, “I have been given al-Kawthar, which is a river flowing across the face of the earth; its banks are domes of pearl and it is not covered. I touched its mud with my hand, and found that it was fragrant musk and its pebbles were pearls”.
Also narrated by Ahmad from Anas, the Prophet (saw) said, “It is a river that Allah (swt) has given to me in Paradise. Its mud is musk and its water is whiter than milk, and sweeter than honey. Birds with necks like the necks of camels drink from it.”
The rivers of Paradise do not just contain water. There are rivers of water, of milk, of wine and of clear honey.
Allah (swt) says: “The description of Paradise which the Muttaqoon have been promised is that in it are rivers of water the taste and smell of which are not changed; rivers of milk of which the taste never changes; rivers of wine delicious to those who drink; and rivers of clarified honey [clear and pure]..” [Muhammad 47:15]
Tirmidhi reports, with a sahih isnaad, from Haakim ibn Mu’aawiyah that the Messenger of Allah (saw) said, “In Paradise there is a sea of honey, a sea of wine, a sea of milk and a sea of water, and the rivers flow out of these seas.” [Jaami' al-Usool, 10/508]
He also told us of a river called Baariq, which flows by the gate of Paradise. During the period of al-Barzakh [the time between death and the day of Judgement] the shuhadaa are beside this river. Ibn ‘Abbaas narrated that the Messenger of Allah (saw) said, “The shuhadaa [martyrs] are in a green dome beside the river of Baariq, near the gate of Paradise, from which provision comes to them morning and evening.” [Saheeh al-Jaami' as-Sagheer, 3/235, no. 3636]