WaAlaykumus Salaam Warahmatullahi Wabarakaatuh,
Allah SWT says in the Quran
“And say to the believing women that they should lower their gaze and guard their modesty; that they should not display their beauty and ornaments except what must ordinarily appear therof; that they should draw their veils over their bosoms and not display their beauty except to their husbands, their fathers, their husbands' fathers, their sons, their husbands' sons, their brothers, or their brothers' sons or their sisters' sons, or their women or the servants whom their right hands possess, or male servants free of physical needs, or small children who have no sense of the shame of sex, and that they should not strike their feet in order to draw attention to their hidden ornaments. And O you Believers, turn you all together towards Allah, that you may attain Bliss.”
[Surah Nur  31]
“O Prophet, tell your wives and your daughters and the women of the believers to draw their cloaks close round them. That will be better, so that they may be recognised and not annoyed. Allah is ever Forgiving, Merciful.”
[Surah Ahzab 59]
Together, these two ayat lay out seven commandments for Muslim sisters:
"to lower their gazes"
"to guard their private parts"
"not to display their beauty except what is apparent of it"
"to extend their headcoverings to cover their bosoms"
"not to display their beauty except to their husbands or their fathers..."
"not to strike their feet (on the ground) so as to make known what they hide"
"to draw their outergarments close around themselves"
As to what consists of a full Hijab [whether or not the face/hands are inculded], there is a difference in the scholarly opinions.
For further reading, IslamQA
WaAlaykumus Salaam :)