Short answer
Marriage in Islam is a simple contract between a man and a woman. Families often help to arrange a match. But the Prophet (ﷺ) commanded that a woman be asked before she is married, and he cancelled a marriage a father forced on his daughter. The husband must give the bride a marriage gift, called the mahr, and it is hers to keep. The contract is witnessed and made public, and most schools of law also require the bride's guardian. Sex outside marriage is forbidden. Men and women are equal before God (﷾) in worth and in reward. The Qur'an promises the same good life to every believer, man or woman, who does good. Husband and wife have rights over each other, and each has duties. The Qur'an calls the bond between them one of love and mercy.
Full explanation
Consent and the marriage gift
The Prophet (ﷺ) forbade marrying a woman without her consent, whether she had been married before or not. When a father married off a daughter who had been married before, against her wishes, the Prophet (ﷺ) declared the marriage invalid. The Qur'an makes the mahr (the marriage gift) the bride's own property. She may give some of it back only if she chooses to.
Abu Huraira reports that the Prophet (ﷺ) said a woman who has been married before is not to be married again without being consulted, and a virgin is not to be married without her permission.
Khansa bint Khidam, who had been married before, reports that her father married her off against her wishes, so she went to the Prophet (ﷺ), and he declared the marriage invalid.
“And give the women (on marriage) their dower as a free gift; but if they, of their own good pleasure, remit any part of it to you, Take it and enjoy it with right good cheer.”
The guardian and the witnesses
The Prophet (ﷺ) said there is no marriage without a wali (the bride's guardian, usually her father). The Maliki, Shafi'i and Hanbali schools of law hold that the guardian must take part in the contract. The Hanafi school lets an adult woman contract her own marriage, though the guardian may object to an unsuitable match. All the schools require the marriage to be witnessed or made public, because a secret marriage is not what Islam means by marriage.
Abu Musa reports that the Prophet (ﷺ) said there is no marriage without a guardian (wali).
Equal before God (﷾)
The Qur'an lists the virtues of believers in pairs, men and women side by side, and promises both the same forgiveness and reward. It promises a good life to whoever does good, man or woman. It describes the first man and woman as made from a single soul.
“For Muslim men and women,- for believing men and women, for devout men and women, for true men and women, for men and women who are patient and constant, for men and women who humble themselves, for men and women who give in Charity, for men and women who fast (and deny themselves), for men and women who guard their chastity, and for men and women who engage much in Allah's praise,- for them has Allah prepared forgiveness and great reward.”
“Whoever works righteousness, man or woman, and has Faith, verily, to him will We give a new Life, a life that is good and pure and We will bestow on such their reward according to the best of their actions.”
“O mankind! reverence your Guardian-Lord, who created you from a single person, created, of like nature, His mate, and from them twain scattered (like seeds) countless men and women;- reverence Allah, through whom ye demand your mutual (rights), and (reverence) the wombs (That bore you): for Allah ever watches over you.”
Rights of husband and wife
The Qur'an says wives have rights like the rights held over them, and that men have a degree above them. Many Muslim scholars tie that degree to the husband's role as head of the household. That role brings added duties, such as paying the mahr and providing for the family. Ibn Abbas was a companion of the Prophet (ﷺ) and an early explainer of the Qur'an in the seventh century. He read that degree as the husband giving up some of his own rights. The Qur'an orders husbands to live with their wives in kindness. The Prophet (ﷺ) told a believing husband not to hate his wife. If he dislikes one of her qualities, he will be pleased with another.
“Divorced women shall wait concerning themselves for three monthly periods. Nor is it lawful for them to hide what Allah Hath created in their wombs, if they have faith in Allah and the Last Day. And their husbands have the better right to take them back in that period, if they wish for reconciliation. And women shall have rights similar to the rights against them, according to what is equitable; but men have a degree (of advantage) over them. And Allah is Exalted in Power, Wise.”
Reports from Ibn Abbas that the 'degree' men have over women is the husband's forgoing some of what is due to him from his wife, and that he would not demand all his rights from her for this reason.
“O ye who believe! Ye are forbidden to inherit women against their will. Nor should ye treat them with harshness, that ye may Take away part of the dower ye have given them,-except where they have been guilty of open lewdness; on the contrary live with them on a footing of kindness and equity. If ye take a dislike to them it may be that ye dislike a thing, and Allah brings about through it a great deal of good.”
Abu Huraira reports that the Prophet (ﷺ) said a believing man should not hate a believing woman: if he dislikes one of her qualities, he will be pleased with another.
Love, mercy and chastity
The Qur'an counts marriage among the signs of God (﷾). Husband and wife find rest in each other, and God (﷾) puts love and mercy between them. Because marriage is the one lawful place for sex, the Qur'an forbids even coming near adultery.
“And among His Signs is this, that He created for you mates from among yourselves, that ye may dwell in tranquillity with them, and He has put love and mercy between your (hearts): verily in that are Signs for those who reflect.”
“Nor come nigh to adultery: for it is a shameful (deed) and an evil, opening the road (to other evils).”
Perspectives
The Islamic perspective
Marriage is a solemn but simple contract, made with a gift to the bride and witnesses. The Prophet (ﷺ) commanded that a woman be asked before she is married. Men and women are equal before God (﷾), and the Prophet (ﷺ) commanded kindness to one's wife.
The four schools of Islamic law agree that the mahr is due and that the marriage must be witnessed or made public. They differ on whether the guardian's part is required. The Hanafi school makes a grown woman's own consent a condition in every case. The Maliki and Shafi'i schools let a father contract a never-married daughter's marriage, but hold that she should still be asked (Bukhari 5136).
The Prophet (ﷺ) commanded that a woman be asked before she is married. He annulled a marriage a father made against his daughter's wishes.
The husband must give the bride a marriage gift, and it belongs to her.
The Prophet (ﷺ) said there is no marriage without a guardian. Three of the four schools of law make his part a condition of the contract.
The Qur'an promises the same forgiveness and reward to believing men and believing women.
Husband and wife have rights over each other. The Qur'an gives the husband a degree above the wife, which scholars link to his headship of the household and his duties to her.
Husbands are commanded to live with their wives in kindness and fairness.
The Prophet (ﷺ) told a believing husband not to hate his wife. If he dislikes one quality in her, he will be pleased with another.
The Qur'an presents marriage as a sign of God (﷾), built on love and mercy, and forbids sex outside it.