Massekhet Shabbat opens with a discussion of the biblical prohibition of carrying out on Shabbat, a topic that is somewhat unexpected, in order to pique the interest of the reader. In terms of the overall framework of the tractate, it would have been more appropriate to begin with later mishnayot.
The prohibited labor to carry out a burden on Shabbat is alluded to in the Torah and explicitly stated in the Prophets. Although it appears in the list of prohibited labors in the Mishna, it constitutes its own discrete unit, and its parameters are significantly different from those of the other prohibited labors. There are two fundamental aspects to the prohibited labor of carrying out. The most significant of these is the prohibition to carry an object from one domain to another, e.g., from the private to the public domain. The definitions of these domains with regard to Shabbat are distinctive, and their parameters are by no means identical to the definitions of domains in other aspects of halakha, neither in terms of their ownership nor in terms of their use.
One only violates the Torah prohibition to carry out on Shabbat if he lifts the object from one place and places it in another place. As is the case with regard to the other prohibited labors, one who performs this action intentionally is liable for the punishment of karet. If he does so unwittingly, he is liable to bring a sin-offering.
Several reasons have been suggested to explain why the tractate opens specifically with the prohibited labor of carrying out from domain to domain. Some explain (e.g. Rabbeinu Tam, the Ran and the Rashba) that the reason is because the tractate, in general, is ordered chronologically and begins with a discussion of matters prohibited immediately when Shabbat begins. One of the matters that requires immediate attention is the prohibition of carrying out, and therefore it was necessary to cite this halakhah first. According to the Penei Yehoshua, since the matter of carrying out is derived from the verse, “A man should not go out of his place” (Shmot 16:29), which is mentioned in the Torah prior to the rest of the prohibited labors of Shabbat, the Sages introduced it earlier in the Mishna.