How did Adam\'s offspring grow? Whom did Adam\'s (A.S) children marry?

How did Adam\'s offspring grow? Whom did Adam\'s (A.S) children marry? What are the significations of the traditions in this regard?
Concise answer
According to the traditions and some interpreters' viewpoints, the current generation of mankind is not from Abel or Cain, it's from Adam's (A.S) other son, Seth. However, when it comes to the marriage of Adam's (A.S) children, there are some viewpoints among Muslim scholars, each mentioning reasons from Quran and traditions for their viewpoints. Some of these viewpoints are briefly mentioned here:
1- It was a marriage among siblings. Since it was not forbidden by God to marry a sibling and because there was no other way to preserve Adam's (A.S) offspring, therefore this type of marriage was acceptable at that time.
2- Since it was impossible for Adam's (A.S) children to marry each other, they married girls from other races and generations living on earth. Then their children became cousins and married among themselves. This view is supported by some traditions as well; since Adam (A.S) was not the first man on earth and he was preceded by other human races.
However, the first viewpoint seems to be more compliant with Quran's text; as some interpreters - like Allamah Tabatabai have advocated.

Detailed Answer
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].

[1]Majlesi, Muhammad Baqer, Beharol Anwar, vol.11, p.244, Dar Ehya at-Torath al-Arabi, Beirut, second impression, 1982
[2]Sheikh Sadooq, Man La YahzorolFaqih, researched and corrected by: Gaffari, Ali Akbar, vol.3, p.382, DaftareEntesharateEslami, Qom, First impression, 1992
[3]See: Ayyashi, Muhammad ibnMasood, at-Tafsir, researched and corrected by: RasooliMahallati, Hashem, vol.1, p.215, al-Matba'atolElmiya, Tehran, First impression, 1959
[4]Beharol Anwar, vol.11, p.226
[5]Sheikh Sadooq, ElaloshSharaye', Davari Bookstore, Qom, First impression, 2006
[6]Tabarsi, Ahmad ibn Ali, al-EtejajelaahlelLejaj, researched and corrected by: Kharsan, Muhammad Baqer, vol.2, pp.314-315, Morteza Publications, Mashad, first impression, 1985
[7]"Sālem ibn Abel Ja'd says: "When Abel was murdered, Adam (PBUH) mourned for a year and did not laugh so when Adam (PBUH) was 130 years old, 50 years after Abel's murder, Eve (S) gave birth to Seth who was Adam's (PBUH) deputy and successor. But Cain was told to go away and be abandoned. He went to Yemen so Satan approached him and said: "Fire swallowed Abel's sacrifice because he worshiped fire so you'd better create a fire for you and your offspring. " Then he built a house of fire and he was the first to set up a fire and worship it. And he made musical instrument s for his children and they drowned themselves in drinking wine, worshiping fire, adultery and vices until God Almighty drowned them with Noah's flood and Seth's offspring survived." Here is the Arabic version of the report:
«قال سالم بن أبی الجعد لما قتل هابیل مكث آدم سنة حزینا لا یضحک ثم أتى فقیل حیاك الله و بیاك أی أضحكک قالوا و لما مضى من عمر آدم مائة و ثلاثون سنة و ذلک بعد قتل هابیل بخمس سنین ولدت له حواء شیثا و تفسیره هبة الله یعنی أنه خلف من هابیل و كان وصی آدم و ولی عهده و أما قابیل فقیل له اذهب طریدا شریدا فزعا مذعورا لا یأمن من یراه و ذهب إلى عدن من الیمن فأتاه إبلیس فقال إنما أكلت النار قربان هابیل لأنه كان یعبدها فانصب أنت أیضا نارا تكون لک و لعقبك فبنى بیت نار و هو أول من نصب النار و عبدها و اتخذ أولاده آلات اللهو من الیراع و الطنبور و المزامیر و العیدان و انهمكوا فی اللهو و شرب الخمر و عبادة النار و الزنا و الفواحش حتى غرقهم الله أیام نوح بالطوفان و بقی نسل شیث»
Beharol Anwar, vol.11, p.220
[8] Quran, al-Nisa verse No.1 «يا أَيُّهَا النَّاسُ اتَّقُوا رَبَّكُمُ الَّذي خَلَقَكُمْ مِنْ نَفْسٍ واحِدَةٍ وَ خَلَقَ مِنْها زَوْجَها وَ بَثَّ مِنْهُما رِجالاً كَثيراً وَ نِساءً...»؛
[9]Beyzawi, Abdollah ibn Omar, Anwarot Tanzil wa Asrarot Ta'weel, researched by: Al-Marashli, Mohammad Abdor Rahman, vol.2, p.58, Darol Ehya le Ehya at-Torath al-Arabi, Beirut, first impression, 2000; Feiz Kashani, Molla Mohsen, al-Asfa fi Tafsir al-Quran, researched by: Derayati, Mohammad Hussein, Ne'mati, Mohammad Reza, vol.1, p.191, Publication Center of Islamic Propagation Office, Qom, first impression, 2000, Makarem Shirazi, Naser, Tafsire Nemoune, vol.3, p.246, Darol Ketab al-Eslamiya, Tehran, first impression, 1995
[10]Tayyeb, Seyyed Abdol Hussein, Atyabol Bayan fi Tafsir al-Quran, vol.4, p.342, Eslam Publications, Tehran, second impression, 1999, Moosavi Sabzevari, Seyyed Abdol A'la, Mawaheb Ar-Rahman fi Tafsir al-Quran, vol.7, pp.249-250, AhlulBayt ('A) Institute, Beirut, second impression, 1988
[11]See: Sheikh Sadooq, at-Tawhid, researched and corrected by: Husseini, Hashem, p.277, Daftare Entesharate Eslami, Qom, first impression, 1977; For more information see: index "Mankind's lifespan from the perspective of the Quran and the Bible" question No.516
[12]TafsireNemoune, vol.3, p.243
[13]Tabatabai, Seyyed Muhammad Hussein, al-Mizan fi Tafsir al-Quran, vol.4, p.135, Daftrae Entesharate Eslami, Qom, fifth edition, 1996