1) the messenger of allah (peace be upon him) said:
((when (the month of) ramadan enters, the doors of heavens are flung open and the doors of hell are shut, and the shayaateen are chained up)).
and in a narration it mentions:
((when (the month of) ramadan arrives, the doors of paradise are opened)).
and in yet another narration, it mentions:
((…the doors of mercy are opened)).
[the authenticity of the above narrations has been agreed upon by al-bukhaaree and muslim]
2) and in the transmission of at-tirmidhee (it mentions):
((a caller would call out: "o you who want good, proceed, and o you who want evil, cease. allah frees people from the fire, and this is done every night until ramadaan is over")).
[al-albaanee has graded it as hasan]
3) and he (peace be upon him) said:
(((the reward for) all the actions of the son of aadam are multiplied (from anywhere between) ten times to seven hundred times)).
and allah (the almighty) said in a hadeeth qudsee :
((…except for fasting, then it is for me and i will give reward for it; he left off his desires and his food for my sake. for the fasting person there are two pleasures: his pleasure at the time of breaking his fast and his pleasure when he meets his lord. and the smell emanating from the mouth of the one who is fasting is better in the sight of allah than the smell of musk)).
[the authenticity of all the above narrations have been agreed upon by al-bukhaaree and muslim]