There is a rift over how Adam's (A.S) offspring survived and how his children married. The main reason behind these different views is different and sometimes conflicting traditions, which have led to different viewpoints in this respect. Here we will mention a few of them.
Continuation of Adam’s (A.S) Offspring and His Children’s Marriage from the Perspective of Traditions
1- There is a tradition saying Adam's (A.S) children first married nymphs from heaven and then they married jinn; Imam Baqer (A.S) says: "Adam (A.S) had four sons. So God sent each of them a nymph from heaven. They married them and had children. Then God reclaimed these nymphs and married those children to four jinns and they had an offspring. So whatever patience there is among mankind is driven from Adam (A.S). Whatever beauty there is among mankind is from those nymphs and whatever vices and misconduct found among mankind is from jinns." [1] This marriage has been narrated in another way i.e. a son married a nymph and another son married a jinn[2]. There is even another tradition narrated with a little difference[3].
2- Imam Reza (A.S) was asked about how Adam (A.S) fathered people. He answered: "Eve (A.S) gave birth to Abel and a twin girl in her first labor. In her second labor, she gave birth to Cain and another twin girl. Abel married Cain's twin sister and Cain married Abel's twin sister. Following these marriages, it was forbidden to marry a sibling[4].
3- A set of traditions stipulate that Adam's (A.S) children never married each other. Instead, they married nymphs sent by God from heaven; such as a tradition where Imam Sadiq (A.S) was asked: How did Adam's (A.S) offspring expand? Because some people say Adam (A.S) was commanded through divine revelation to marry out his daughters to his sons and people's forefathers and foremothers are those brothers and sisters. Imam Sadeq (A.S) answered: "God Almighty is greater than to say such things about Him. Has He created prophets (A.S), apostles, religious men and women and Muslim men and women from haram [forbidden] not having enough power to create them through halal [permissible] means or He has taken a covenant from man for purity and cleanness from sins…. Then Imam Sadiq (A.S) described how Adam's (A.S) offspring expanded and said:"When Abel was murdered by Cain, Adam (A.S) mourned and lamented on the death of his son… And God Almighty granted him Seth (A.S) alone without a twin sister. Seth's name is Hebatollah [A gift from God] and he is the first man to become the deputy and the successor to a prophet. After Seth (A.S) God granted Adam (A.S) with Japheth without a twin. When they reached puberty and God decided to expand Adam's (A.S) offspring as you see (they have reproduced) while marriage between siblings was forbidden. Therefore God sent a nymph called Nazalah from heaven on a Thursday evening and commanded Adam (A.S) to marry her to his son, Seth. Then next day in the evening, God sent another nymph called Monzalah and commanded Adam (A.S) to marry her to Japheth. Once Adam (A.S) married those two nymphs to his sons, Seth (A.S) had a son and Japheth had a daughter. When those two reached puberty God commanded Adam (A.S) to marry Japheth's daughter to Seth's (A.S) son, Adam (A.S) obeyed and made them husband and wife from whom God's prophets, messengers, elites and their offspring are[5].
4. In a dialogue with a man from Quraysh, Imam Sajjad (A.S) said:"Abel married Lozaq, Cain's twin sister, and Cain married Eqlima, Abel's twin sister." Qurayshi man asked:" Did Abel and Cain impregnate each other's sisters?" Imam (A.S) said:"Yes" Man said:"That is an act practiced by Magianists today." Imam (A.S) said:"Magianists practice this act while we have negated it, is because they practice this action after God has forbidden it." Then Imam Sajjad (A.S) added that:"Do not reject this fact because permissibility of this action at that day and its impermissibility today are both God's commands. Has not God created Adam's (A.S) wife from himself while we see God made her halal for him, so this was the ruling of shari'ah for Adam's(A.S) son, exclusive for them. Later on God Almighty revealed His ruling to forbid such a marriage[6]."
5. According to some traditions; expansion of Adam's (A.S) offspring is considered from Adam's (A.S) third child called Seth or Hebatollah, Adam's (A.S) deputy and successor; since Abel was murdered by Cain, and Cain was outcast because of sin and disobedience, he committed sins and vices which made his children and offspring to follow him and be destroyed in Noah's flood[7].
In short, the issue of  the marriage of Adam's (A.S) children is amongst issues about which there are conflicting traditions in Hadith collections.
Interpreters' Viewpoints
Having referred to the following verse “O! People! Be careful of (your duty to) your Lord, Who created you from a single being and created its mate of the same (kind) and spread from these two, many men and women“ [8] some interpreters believe that: The growth of Adam's (A.S) offspring has taken place only through Adam (A.S) and his wife without the involvement of a third party[9]. This necessitates that Adam's (A.S) children have married each other – brothers and sister - because if they had married from another race and other wives for Adam (A.S), God's words "from these two" would not be true.
This issue has been the subject of numerous traditions without much surprise; since based on an argument narrated in some traditions this type of marriage had been permissible because the ruling to forbid marriage of siblings had not been revealed.
Obviously a forbidden action depends on whether God has forbidden it or not. What is wrong with it if, due to some necessities and expediencies, something is permitted during a specific period of time and it is forbidden later? As we read in a tradition by Imam Sadiq (A.S) (as mentioned in tradition no.4)
On the contrary, however, some interpreters[10] accept the contents of those traditions stipulating that Adam's (A.S) children never married their sisters rather they married nymphs sent by God from heaven; such as the tradition narrated from Imam Sadiq (A.S) (tradition no.3)
There is another possibility that Adam's (A.S) children married with humans before the generation of Adam (A.S); because according to some traditions[11] Adam (A.S) was not the first man on earth and he was preceded by other humans. Modern scientific studies also indicate that human species have lived probably for quite a few million years while it has not been so long since Adam (A.S) set foot on earth. Therefore it should be accepted that man was preceded by other humans who were on the verge of extinction when Adam (A.S) was created, there is nothing wrong with this assumption that Adam's (A.S) children may have married with humans remaining from previous species however this possibility does not much comply with the denotation of the above verse from the Quran[12].
It can be concluded that the first viewpoint by interpreters complies more with the denotation of the Quran; as some interpreters such as Allamah Tabatabai has emphasized on this possibility and has accepted it[13].

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