Mishneh Torah — Transmission of the Oral Law מסירת תורה שבעל פה, Chapter 3

וְהַמִּצְוָה, שְׁהִיא פֵּרוּשׁ הַתּוֹרָה – לֹא כְתָבָהּ; אֵלָא צִוָּה בָּהּ לַזְּקֵנִים וְלִיהוֹשׁוּעַ וְלִשְׁאָר כָּל יִשְׂרָאֵל, שֶׁנֶּאֱמָר "אֵת כָּל־הַדָּבָר, אֲשֶׁר אָנֹכִי מְצַוֶּה אֶתְכֶם – אֹתוֹ תִשְׁמְרוּ, לַעֲשׂוֹת . . ." (דברים יג, א). וּמִפְּנֵי זֶה נִקְרֵאת תּוֹרָה שֶׁבְּעַל פֶּה.

"The mitzvah" - i.e., the explanation of the Torah - he did not transcribe. 60b, which prohibits writing down the teachings of the Oral Law. Nevertheless, from the Rambam's statements here and in the Introduction to his Commentary on the Mishnah, it appears that the prohibition only applies to the composition of a text from which to teach, and not writing down notes for one's personal study. Instead, he commanded it [verbally] to the elders, to Joshua, and to the totality of Israel, as [Deuteronomy 13:1] states: "Be careful to observe everything that I prescribe to you." For this reason, it is called the Oral Law.