The following are some of my thoughts on the word תולדות which is arguably the מילת מנחה, leitwort (see this chapter from Rabbi Yitzchak Etshalom's book, Between the Lines of the Bible also see this article concerning Prof. Yehuda Elitzur's methodology)
of ספר בראשית.
אֵלֶּה תוֹלְדוֹת הַשָּׁמַיִם וְהָאָרֶץ
What does the תורה mean when it uses the phrase "אלה תולדות"1? An analysis of most of the examples of this word in תנ"ך would suggest that it introduces the genealogy of a particular person (for future reference, we will call these the "simple cases"). However, one only need look as far as the first appearance of this word in the חומש (B'reishit 2:4) to recognize the shortcomings of this translation.
ד אֵלֶּה תוֹלְדוֹת הַשָּׁמַיִם וְהָאָרֶץ, בְּהִבָּרְאָם: בְּיוֹם, עֲשׂוֹת ה' אֱלֹקים--אֶרֶץ וְשָׁמָיִם.
These are the תולדות of the heavens and the earth: on the day Hashem, God made, earth and heavens.
Simply put, Heavens and Earth do not have children. It can be suggested that in this case, תולדות is being used poetically - true, Heavens and Earth do not have children in the literal sense, but, figuratively, Adam and Chava are children of the Earth - being formed from the ground - and children of Heavens - G' "blew" the breath of life into their nostrils2. However, this only begs the question - why use this figure of speech?
I believe the point is to take our focus off Adam and Chava and place it on the "grand scheme of Creation". The תורה is trying to tell us what here is most significant. The story of גן עדן is not fundamentally about Adam and Chava. Rather, it is the story of how the Heavens and Earth develop into their most excellent product, mankind - even with all its shortcomings.
This gives us a new insight into how to understand this word in the "simple cases". "אלה תולדות" points to the most significant products resulting from a man's efforts - children (and, in every case, at least, grandchildren). What about all of a person's great deeds? Can they not be more significant than children? The truth is, as great as a person's deeds might be, if he has no child to inherit him and continue in his ways all his great deeds will be but a memory. As our father Avraham says (15:2-3),
ב וַיֹּאמֶר אַבְרָם, אֲדֹנָי ה' מַה-תִּתֶּן-לִי, וְאָנֹכִי, הוֹלֵךְ עֲרִירִי; וּבֶן-מֶשֶׁק בֵּיתִי, הוּא דַּמֶּשֶׂק אֱלִיעֶזֶר. ג וַיֹּאמֶר אַבְרָם--הֵן לִי, לֹא נָתַתָּה זָרַע; וְהִנֵּה בֶן-בֵּיתִי, יוֹרֵשׁ אֹתִי.
Avram said, my Master, Hashem, what shall you give? I go about barren and the steward of my house, he is the Damascene, Eliezer. And Avram said, "Behold, to me you have given no seed, and a member of my household will inherit that which is mine.
One major question is why are there no תולדות אברהם? Throughout ספר בראשית shortly after the תורה mentions the death of an "אב תולדות" it begins the next "אלה תולדות"3. The תולדות תרח must end when he dies (11:32). I believe the answer is simple. At that point in the narrative אברהם is, in fact, a different person אברם. This אברם can not have תולדות because his wife is barren:
כט וַיִּקַּח אַבְרָם וְנָחוֹר לָהֶם, נָשִׁים: שֵׁם אֵשֶׁת-אַבְרָם, שָׂרָי, וְשֵׁם אֵשֶׁת-נָחוֹר מִלְכָּה, בַּת-הָרָן אֲבִי-מִלְכָּה וַאֲבִי יִסְכָּה. ל וַתְּהִי שָׂרַי, עֲקָרָה: אֵין לָהּ, וָלָד.
Avram and Nachor took for themselves wives; the name of the wife of Avram, Sarai; the name of the wife of Nachor, Milka, daughter of Haran, father of Milka and father of Yiska. And Sarai was barren; she had no offspring.
It is interesting to note that the תורה redundantly uses the expression, " אֵין לָהּ, וָלָד", translated here as, "she had no offspring" as opposed to the equally meaningful "אין לה בן" . The word used for offspring is " וָלָד" from the shoresh, י.ל.ד, the same shoresh of תולדות, reinforcing our suggestion that אברם has no תולדות. This begs the question, once again - why not begin תולדות אברהם once his name is changed and he has children4? I believe the תורה is teaching a significant idea about אברהם. All of the other אבות5 in ספר בראשית are biological אב to their children and as an outgrowth of this role the spiritual/intellectual אב of his children and grandchildren and so on. The phrase "אלה תולדות" includes within its scope those events that directly bear upon his biological descendants and bear the stamp of his intellectual/spiritual אבהות/מנהיגות, fatherhood/leadership. Those תולדות end when the next אב becomes independant of his own father. Concerning אברהם, however, the תורה does not want to limit his impact to only his biological descendants. This seems to be indicated in Hashem's first ברכה of אברהם(B'reishit 12:3):
ג וַאֲבָרְכָה, מְבָרְכֶיךָ, וּמְקַלֶּלְךָ, אָאֹר; וְנִבְרְכוּ בְךָ, כֹּל מִשְׁפְּחֹת הָאֲדָמָה.
And I will bless those who bless you and he who curses you, I will curse; and through you will be blessed all the families of the earth.
"All the families of the earth" are to be blessed through אברהם through his intellectual/spiritual legacy - this is not limited to his biological descendants. The רמב"ם discusses this idea in one of his תשובות to עובדיה הגר, Ovadia the Proselyte (here is a link to the complete תשובה)
פריימן, הוצאת "מקיצי נרדמים", התרצ"ד, סימן מב
...נמצא שאברהם אבינו ע"ה הוא אב לזרעו הכשרים ההולכים בדרכיו ואב לתלמידיו וכל גר שיתגייר. לפיכך יש לך לומר "אלוקינו ואלוקי אבותינו", שאברהם ע"ה הוא אביך. ויש לך לומר "שהנחלת את אבותינו", שלאברהם ניתנה הארץ, שנאמר "קום התהלך בארץ לארכה ולרחבה, כי לך אתננה" (בראשית יג,יז)
Avraham, our father, is the father of his uncorrupted children who follow his ways. He is the father to his students and to every convert. Therefore, in your prayers you should say, "Our G' and the G' of our forefathers", because Avraham is your [referring to Ovadia] father. You should also say (in the Birkat HaMazon), "Who caused your forefathers to inherit...", because the land was given to Avraham, as it says, "Get up, traverse the land by its length and width, for I give it to you." (B'reishit 13:17).
1And in one case, "זה ספר תולדות אדם" (B'reishit 5:1).
2This possibility is suggested in the דעת מקרא.
3See, B'reishit 6:9, 10:1, 11:10, 11:27, 25:12, 25:19, 36:1, 36:9, 37:2. 2:4, the introduction to the story of Gan Eden and 5:1, the introduction to the genealogy of Adam down to Noach obviously can not bear this characteristic.
4It is not unusual for תולדות to begin even after all or some of an אב's children are mentioned - see, 5:1, 10:1, 11:10 and most notably, 6:9, 11:27 and 37:2.
5I use this term in its broader sense to include not only Yitzchak and Ya'akov, but also, Noach, Shem, Cham, Yefet, Terach and Yishmael and Eisav.