Genèse 6:18

But I will establish my covenant with thee; and thou shalt go into the ark, thou, and thy sons, and thy wife, and the wives of thy sons with thee.

AND I WILL ESTABLISH MY COVENANT. Rabbi Abraham ibn Ezra said that this is a sign that G-d had sworn to Noah that during the flood, neither he nor his children would die even though it is not clearly written at first. This is similar to what we find in Deuteronomy: And ye came near unto me every one of you, and said: Let us send men before us, that they may search the land for us. Ramban cites this as another case where the first account lacks some of the details of the later account.
The meaning of V’hakimothi (And I will establish) is “I will fulfill My oath.” It appears likely to me that this covenant mentioned here refers to the rainbow, [Thus G-d hinted to Noah that after the flood He will make a covenant with him if he will fulfill the commandment concerning the making of the ark.] The meaning of the word b’rith (covenant) is an agreement and accord which two have chosen, stemming from the root, ‘b’ru’ (choose) you. And the word b’rith takes the same form in construct and in separateness. A similar case is [the word sh’vith, captivity]: ‘sh’vith’ (the captivity of) Jacob; is in construct. And his daughters ‘bash’vith’ (in captivity). is separate. And some say that the word b’rith means the establishment of a boundary [to which each party to the covenant should adhere]. All these are Abraham ibn Ezra’s words.
A more correct explanation in line with the simple meaning of Scripture is that the purport of the expression, And I will establish My covenant, is, “At the time of the coming of the flood, My covenant will be established with you so that you and your family and two of all flesh will come into the ark to remain alive, that is to say, so that you will live there and maintain yourself in order to go forth from there alive.” And b’rith (covenant) means G-d’s word when He decrees something without any condition and residuary and fulfills it. Now He mentions the b’rith and mentions that it will be fulfilled, [which, according to the present interpretation is an apparent redundancy], just as we find the verse, The Jews ordained and took upon them, and upon their seed, meaning they accepted upon themselves a matter which was to exist. [Thus our verse is to be explained in a similar way, i.e., He established an unconditional covenant.]
By way of the truth, [the mystic lore of the Cabala], the b’rith is everlasting, the word being derived from. In the beginning G-d ‘bara’ (created). Thus brithi (My covenant) is similar to b’riyothi (My creation), and the word is alike in construct form because it is adjoined to the times there were before us. He thus commanded that the b’rith exist and be with the righteous one [Noah]. In a similar sense are the verses: As for Me, behold, I establish My covenant with you; My covenant was with him. The learned student [in the mystic lore of the Cabala] will understand.

והקימותי את בריתי, a reference to the covenant G’d made with Noach after the deluge.

והקימותי את בריתי אתך, the covenant that I am going to make with you as part of the deal that you and your family will be saved. I will keep this promise for you and your descendants.

ובאת אל התבה, the ark in which I told you that I would save you from the waters of the deluge.

אתה ובניך, the absence of a reference to the females, shows that copulation was forbidden in the ark, seeing that the women were to have separate quarters. (Chulin 70) G’d separated them by writing: אתה ובניך, אשתך ונשי בניך, The moral lesson in all this is that a time when the entire human species is being wiped out, it is not appropriate for the survivors to indulge in physical pleasures. All they were allowed to do was to eat enough in order to keep themselves alive and well.