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Rabbi Yehudah haNasi compiled all of Jewish law into six orders (sedarim, sing: seider) of 73 tractates (mesechtos, sing: mesechta). There is one exception, the laws of Chanukah, which were probably omitted because they were already codified as the appendix to Megillas Ta'anis, a scroll (megillah) listing minor holidays upon which fasting (ta'anis/ta'anit) is prohibited.
In general, each mesechta sticks to a single topic. However, there is drift, such as the inclusion of a second law that was included in the same quote as the first. (There is a long run of these in Mes. Yuma, which starts with "There is no difference between Yom Kippur and Shabbos [with respect to the laws of rest], except..." and then goes on with other, non-Yom Kippur, "There is no difference between..." mishnayos.)
There is also mesechtes Ediyos (mesechtes = the mesechta of), which is organized because of a date, not the topic. Rabban Gamliel ran the yeshiva so that it included only the best and the brightest. He was deposed (later to be partly reinstated), and on the day he was deposed, they recorded the testimonies (ediyos) given by people who were excluded from the study hall all those years.
These exceptions serve a purpose, though. It allowed Rav Yehudah haNassi (also called "Rebbe") to include those laws that weren't on topics broad enough to warrant their own books. While he strove for completenetss, it's impossible (as I'm sure Rebbe also knew). There were gaps in his compilation, or at least laws he thought we could deduce from what was there that we found required explicitly statement. These were then compiled into mesechtos qetanos (small tractates), later collections of tannaitic statements.
What you describe as six topics of books are really six broad categories of law under which there are multiple books.
Of Rav Yehudah haNasi's original mesechtos, there has been only slight modification to his structure. The first mesechta of seider Neziqim (damages) was very long, so we broke it up into three sections, called Bava Qama (first gate), Bava Metzi'ah (middle gate), and Bava Basra (last gate). On the other hand, he had three tiny tractates on the laws of Passover which we since combined into one.
Of the six orders, "zera'im" has one tractate, Berachos, about blessings and prayers, and the rest is laws about farming Israel. In the diaspora, little of it applies. Similarly, the last order, "qodshim" (sacred things), is largely about Temple worship. So, of the six orders, only four of them are applicable in the majority today.
When Rav Yaaqov ben Asheir chose to codify Jewish law, he wrote the Arba Turim (four rows, a reference to the rows of gems on the high priest's breastplate in the temple). The same structure of four turim was used by R' Yosef Caro when compiling the Shulchan Arucha. He took these four orders, added the parts of the two remaining ones here and there, but basically based himself on Rebbe's structure.
The four turim are:
Orach Chaim (way of life): The laws of prayer (from zera'im's Mes Berachos), tefillin and tzitzis (from Qodshim's tractate Chullin) Shabbos and holidays (from Mo'eid).
Yoreh Dei'ah (enlighten with knowledge: Laws of kashrus and sexuality. This is from the last two orders, Taharos, and Chullin in Qodshim.
Even ha'Ezer (rock of the Helper, see Sam I 5:1): marriage and divorce (Nashim, which is after Mo'eid in the mishnah).
Choshein Mishpat (breastplate of judgement): court and fiscal law (Neziqim).
This illustrates how the structure Rebbe gave, albeit heavily ammended, was intended to include everything, not simply six topics.
By the way, the word "mishnah" (lit: that which was repeated) predates the comilation. It was a study style. In the days of a purely oral law, it was common to reduce the study of the law into easily memorizable epigrams. Rebbe reduced these to a more canonical form, and organized them into a hierarchy of sedarim, mesechtos, and chapters.
One last, relatively unknown, tidbit. The Tosafists write (I believe it's a statement by Rabbeinu Tam in particular) that Rebbe did not actually write the mishnah. While he did redact and compile the collection, they believe that he did not publish them. In their opinion, the notion of printing what should ideally be an oral, dynamic, Torah wasn't considered necessary until centuries later, slightly before the talmuds were compiled.
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