One of the earliest authorities to deal with this question was Rav Chaim Avraham Miranda who writesin his sefer Yad Neeman (Salonica 5564 p. 1a–2a)  as follows:

“Since the law of lighting Chanukah candles was established long before Rabbeinu HaKadosh why did he not mention explicitly in the Mishnah its time its laws and the obligation as [he did for the laws of] megillah [the washing of the] hands and eiruv?

“My meager intellect was later assuaged when I saw the Rambam’s words in Menachos at the beginning of Perek HaTecheiles: ‘The Mishnah does not speak about the laws of tzitzis tefillin and mezuzah….  The reason for this… is that these things were common knowledge at the time that the Mishnah was composed and they were known and practiced by all the people … Therefore he did not see fit to speak about them…but the Gemara was composed to explain it.’”

The Chasam Sofer in his chiddushim on Maseches Gittin (78a) gives the same answer regarding the absence of Chanukah from the Mishnah. Riach Ibn Samon notes in support of this explanation that  Rabbeinu HaKadosh lived shortly after the destruction of the Second Beis HaMikdash and very little time had passed since the era of the Chashmonaim. Thus the entire subject of Chanukah was still a matter of widespread common knowledge ( Eidus B’Yehosef sec. 15).

Yet the laws of Purim were certainly no less well-known than those of Chanukah. Nevertheless the holiday of Purim is the subject of an independent tractateIn addition it should be noted that some  commentators disagree with Rambam’s explanation of why the laws of tefillin tzitzis and mezuzah were not included in the Mishnah. They point out that the average Jew was not in fact familiar with many of those laws and some  were not even known to erudite Torah scholars (see Menachos 41a). They suggest instead that  that Rabi Yehudah HaNasi simply omitted those halachos because they were also not included in the original version of the Mishnah compiled by Rabi Akiva which left them out either for the sake of brevity or for some other reason unknown to us.

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