Regular Vows
A man that makes a vow to Hashem or swears and oath to prohibit himself, shall not violate his word, making it mundane.[2] He must do do whatever came out of his mouth. An example of a vow is someone that says; it should be prohibited upon him just like a sacrifice, that he will not eat, or do a certain thing.[2] One can only make an oath to prohibit upon himself something that is curranty permissible for him. However he can not make an oath to do something that is already prohibited on him, like taking an oath to eat nivelah carcasses.[2]

Vows by a Narah
A woman in her youth that makes a vow to Hashem and imposes a prohibition upon herself while she is still under her father's jurisdiction, even if she is not actually living in his house,[3] the vow can be absolved by her father. This is only true when she is neither a minor or an adult. If she was a minor then her vows are not counted and once she is an adult over the age of 12.5 years old, then she is no longer under her father's jurisdiction. This stage is called a 'Narah' and begins at the age of 11 for smart girls who know in whose name they vowed. For regular girls it starts at age 12[3] and ends a half a year later when they reach adulthood at age of 12.5.

If her father heard her vow or prohibition that she had prohibited upon herself, and remains silent, then all her vows will apply, any prohibition that she has imposed upon herself will remain in place. When an expert absolves a vow he must express it as a 'Hatara',[1] a retroactive release loophole. When a husband or father absolves a vow he must express it as a 'Hafara',[1] an absolution where the current vow is dissolved. If either uses the other terminology, it will not take effect.[1] If her father blocks[4] her and nullifies[4] her vow on the day he hears it, then all her vows and prohibitions that she has imposed upon herself no longer remain. Hashem will forgive her because her father stopped her. This includes even a case where a husband absolved the Nazarite vow of his wife and despite that she was not aware of this, she transgress what she believes is her existing vow by drinking wine and coming in contact with the dead.[4] If such a case where the vow was revoked, requires forgiveness from Hashem, then certainly in cases where active vows have been transgressed.[4]

A woman who becomes halachically engaged[5] and has outstanding vows or prohibitions that she self-imposed through an utterance of her lips. These were made when she was still in her father's home, but her father did not hear about them, therefore, they were neither revoked nor upheld.[5] If her husband hears about these vows or prohibitions and chooses to remain silent on that day, then her self-imposed vows and prohibitions will continue to be in effect. If her husband explicitly endorses it, then the vow will certainly remain valid.[6] If her husband, along with her father,[7] annuls her vow on the day he learns of it, then the vow is nullified and Hashem will forgive her. Once a woman is Halachically engaged then both her father and husband must nullify her vows. If the father revoked it and the husband did not, or vice versa, then the vow is not nullified. It goes without saying that if one of them upheld the vow, then the other can not nullify it.[5]

If a widow or divorcee makes a vow prohibiting herself then that will remain active, since she is not in the jurisdiction of her father or a husband.[8] This is only true if her husband died after they actually got married. If her husband died only after their halachic engagement, then she returns to her father's jurisdiction.[8] 

A married[9] woman that makes a vow or imposes a prohibition upon herself with an oath while in her husbands house and jurisdiction. If her husband heard and remained silent and did not block her, then all her vows and every prohibition she imposed upon herself remain active. If her husband nullified them on the day he hears them, then all the vows that were issued from her lips and self imposed prohibitions are canceled and Hashem will forgive her. 

A husband can uphold or nullify and vow or oath of self affliction made by his wife. He can not nullify the vows of his wife that are not related to self-affliction.[10] However, if her husband remained silent from day to day and upheld all the vows and prohibitions that his wife made, then these vows remain active since he remained silent on the day he heard about it. The husband has only until the end of that day to nullify the vow, rather then a full 24 hour period.[11] If he hears about it at the start of the night, he has a full 24 hours. However if he hears about it right before nightfall, then he has only a window of a few minutes.

If the husband nullifies the vow after he already heard it and endorsed it,[12] even if it is still on the first day,[12] he will bear the responsibility of the sins caused by his wife violating the vow. He will take her place for receiving the punishment, as is the case in cases where someone causes his friend to stumble[12] and sin. These were the laws that Hashem commanded Moshe regarding man and his wife and a father regarding his daughter while she is still in her youth in her father's house.

Hashem spoke to Moshe and told him to take revenge for the Jews against the Midianites. Afterwards Moshe will pass away. Only the Midianites were to be targeted but not against the Moabites. Moav had acted out of fear of being plundered by the Jews who had been commanded only not to battle them. Midyon on the other hand had no reason to involve themselves in this fight.[13] Additionally Moav was spared in merit of the two good convert doves that would later come out of them; Rus the Moabitess and Naamah the Ammonitess.[13]

Despite the fact that Moshe knew his death was dependent on this battle, he immediately and joyously[14] instructed the Nation to dedicate righteous[14] soldiers and arm[14] them to do battle. So they can carry out the revenge of Hashem against Midayan, for however opposes the Jews it is as if he opposes Hashem.[14]  1000 soldiers were dedicated from each tribe, from all the Jewish tribes, including the Tribe of Levi[15] and were sent to the army. 

1000 armed soldiers from each tribe were given over, totaling an army of 12,000. When the soldiers  found out that Moshe would pass away after the vengeance on Midyan, they refused to go, until they were forced to do so.[16] This proves how much the Jews like their leaders, even though when Moshe was still alive, at one point he was afraid of being stoned.[16] 

Moshe sent the 1000 soldiers from each tribe to the army, along with Pinchas the son of Elazar the Kohen who was equivalent to all of them.[17] In his possession[17] were the holy Aron and Tzitz vessels along with blowing trumpets. Pinchas led the war instead of his father Elazar since he was the Mashuach Milchama - the Kohen anointed for the war.[17] Additionally he was the one how began this mitzvah by killing Kuzbi and was therefore given the merit of completing it.[17] Pinchas' mother was a daughter of Putiel who descended from both Yisro who fattened calves for idolatry and Yosef who  grappled and prevailed over his evil inclination. Pinchas therefore went to take revenge for his great grandfather Yosef who was sold into slavery by the Midanites.[17]

They mounted an attack against Midian as Hashem had commanded Moshe. They killed every male. Bilam had returned to Midyan to claim his reward for his advice that lead to the death of 24,000 Jews.[18] They paid him in full and did not cheat him.[18] Bilam then traveled from Midyan to meet the Jews and offering them harmful advice;  how can they expect to win with only 12,000 soldiers when previously they could not overcome the Midyanites with their full 600,000.[18]

During the battle, Bilam used sorcery to levitate himself and the Midianite kings allowing them to fly in the sky. When they were shown the Tzitz with the name of Hashem engraved on it, they fell from the air down to earth upon the carcasses of their slain troops.[17] The Jews killed the five kings of Midyan Evi, Rekem, Tzur, Chur, and Reva. All these 5 kings were all equally involved in the conspiracy against the Jews, and now they all received the same punishment.[18] Bilam the son of Beor, they killed by sword.  Bilam had disregarded his own skill of the sword, instead adopting the Jewish strength of prevailing through prayer and speech in his attempt to curse them. In response, the Jews leveraged the Gentile's skill of battle through swordplay against Bilam.[18] 

The Jews took the Midianite women and children captive. They plundered all their animals, livestock and all their movable possessions that were not jewelry.[20] They they set fire to all their residential cities and their castles where their law making priests and ministers resided.[19] They took all the booty of movable garments and jewelry,[20] as well as the human and animal plunder. By the Jews even their warriors are all righteous,[20] and were not suspected of stealing and taking anything without permission, therefore they brought forward 100% of the booty.[20] They brought the captives, plunder and booty to Moshe and Elazar the Kohen and to all the Jews in the camp on the plains of Moav by the Yericho section of the Yarden river.

[2] Rashi Bamidbar 30:3

[3] Rashi Bamidbar 30:4

[4] Rashi Bamidbar 30:6

[5] Rashi Bamidbar 30:7

[6] Rashi Bamidbar 30:8

[7] Rashi Bamidbar 30:9

[8] Rashi Bamidbar 30:10

[9] Rashi Bamidbar 30:11

[10] Rashi Bamidbar 30:14

[11] Rashi Bamidbar 30:15

[12] Rashi Bamidbar 30:16

[13] Rashi Bamidbar 31:2

[14] Rashi Bamidbar 31:3

[15] Rashi Bamidbar 31:4

[16] Rashi Bamidbar 31:5

[17] Rashi Bamidbar 31:6

[18] Rashi Bamidbar 31:8

[19] Rashi Bamidbar 31:10

[20] Rashi Bamidbar 31:11