Is there a weekly mitzvah to learn שנים מקרא? For example, if someone hypothetically missed בראשית is there a separate mitzvah to learn נח, or is it all or nothing?

The obligation to complete the weekly Parsha is mentioned in gemara [1] which states לעולם ישלים אדם פרשיותיו עם הצבור שנים מקרא ואחד תרגום. The gemara adds that one must learn the Parsha corresponding to the leining of that week - ובלבד שלא יקדים ולא יאחר. This is codifies by the Shulchan Aruch.[2] The Aruch Hashulchan [3] claims that this requirement is coupled together with משה רבינו‘s enactment of קריאת התורה [4]. Because one is meant to complete the Parsha בציבור, Rabbeinu Yonah [5] believes that one should complete this obligation prior to the Krias Hatorah in Shul. Tosfos [6] cites the Midrash that Rebbi instructed his children to complete the Parsha prior to eating the Shabbos day meal.[7] The Tur [8] cites this Midrash but he adds that if one ate before finishing the Parsha, he should complete the Parsha before Mincha, when the next Parsha is first read. The Beis Yosef [9] notes that the language of the Tur implies that one can no longer fulfill his obligation after Mincha and this is in fact the view of the Kol Bo.[10] He goes on to cite a dissenting view that one may complete the previous Parsha up until Wednesday. Finally, he cites רבינו שמחה that one may complete a missing Parsha up until Simchas Torah.[11]

The Shulchan Aruch [12] cites each of these four opinions, ideally before סעודת שבת, before Mincha,[13] by Wednesday, finally before Simchas Torah when the "ציבור" completes the entire Torah. Based on the above, if one misses a Parsha he should certainly make it up in accordance with the last two options mentioned by the Shulchan Aruch. Additionally, even if one should entirely miss a Parsha or two, he should most certainly learn and complete all the other Parshiyos. The Poskim [14] discuss the proper order of Parshios when one catches up. If one has yet to complete בראשית should do so prior to reading נח or should first complete נח and then return to בראשית? R’ Shlomo Zaman [15] writes that it is best to complete the previous Parsha first but if one began the next Parsha already that too is acceptable as one need not read the Parshiyos in order.[16]

[1] Brachos 8a

[2] 285:1

[3] 285:2

[4] See B”K 82a, Rambam Tefilla 12:12

[5] Brachos 4b d.h. L’Olam. The Ohr Zarua Shabbos 42:1,2 appears to agree with this notion. See Mishnah Berurah 285:9.

[6] D.h. Yashlim.

[7] See Biur Halacha d.h. Yashlim who cites the Ohr Zarua who explains that if one waits to learn the Parsha until after eating the meal he may neglect learning the Parsha.

[8] 285

[9] 285:4

[10] 37

[11] See Hagaos Maimonios Teffilah, 13:25

[12] 285:4

[13] See Halichos Shlomo Tefillah 12:35 who adds that one’s personal Mincha is the cutoff point. He adds (footnote 46) that if one is unable to finish before Mincha he should try and finish before Shabbos is over.

[14] Teshuvos Maharsham 1:213, B’Tzel Hachochmah 1:9

[15] Halichos Shlomo Tefillah 12:36

[16] But it is certainly best to complete the current Parsha that week as well as according to Rabbeinu Chananel שנים מקרא is to familiarize oneself with the upcoming Krias Hatorah (see Terumas Hadeshen 23, Haghos Maimonios, Tefillah 13:300).