[I] MISHNAH AND BARTENURA
(a) MISHNAYOS KINIM (or Kanim) are considered to be among the most difficult Mishnayos in all of Shas. This is due to the difficulty of some of the Halachic aspects of the laws of Kinim, as well as to the difficult mathematical calculations necessary to fully grasp their ramifications. Nonetheless, it is only the last three Mishnayos of the third (and last) chapter that pose the main difficulty of the Maseches. The many Rishonim that have written on this Maseches each suggest their own approach to these difficult Mishnayos.
Even though those who printed the Shas put Kinim immediately after Me'ilah, its proper place is actually at the end of Seder Kodshim, following Midos. That is indeed where it is printed in the volumes of Mishnayos, and the Rambam places it there as well in his introduction to Perush ha'Mishnayos. (That this is the proper order is also apparent from the atypical Agaddic ending of the last Mishnah in Kinim. Further evidence is supplied by the fact that Kinim only has three Perakim, making it the smallest Maseches in Kodshim. In all the other Sedarim the smallest Maseches is saved for last -- see what we wrote about this in our Introduction to Tamid.)
Since there is no Gemara written on Kinim, we will not be writing any INSIGHTS or BACKGROUND notes on Kinim. Rather, we will write REVIEW QUESTIONS and their ANSWERS. The questions will be prepared based on Mishnayos Kinim with the commentary of the Rav (Bartenura), and minor additions from the commentary of the Tiferes Yisrael.
(b) RAV - Rav Ovadiah of Bartenura, printed in the Mishnayos. As was his style, most of the commentary is based on the words of the Rambam and the Rosh.
[II] RISHONIM
(a) MEFARESH - The identity of this Rishon is not entirely clear. It may, however, be guessed that he is the author of the Perush on Tamid as well, see what we wrote at the beginning of Maseches Tamid concerning the identity of this Rishon.
(b) TOSFOS - A few short comments of Tosfos on Kinim were published in our volumes of the Shas.
(c) ROSH - Printed in our volumes of the Shas, the Rosh's commentary on Kinim is concise and sufficient. It is recommended that those who are learning Kinim from the Mishnayos printed in the Shas should learn it with the commentary of the Rosh or the Mefaresh (see (a)).
(d) PERUSH HA'RAZAH - the Ba'al ha'Maor, Rabeinu Zerachya ha'Levi.
(e) PERUSH HA'RA'AVAD - This commentary was apparently written by the same Ra'avad who wrote the Hasagos on the Rambam. In the Perush of the Ra'avad to Toras Kohanim (Tazria, Perek 4 end of Beraisa 3), the Ra'avad mentions that he discussed a certain point in a pamphlet that he wrote explaining the Mishnayos of Maseches Kinim. (However, the point in question does not appear in the commentary that we have before us.) See what we wrote further about the Perush ha'Ra'avad in our Introduction to Maseches Tamid.
The two commentaries of the Ra'avad and Razah are so lengthy that the printers of the Shas were only able to print alongside the Mishnayos the first Perek of their Perush. Their rest of their Perush can be found at the end of the Maseches. These two commentaries are both printed in the Vilna Mishnayos as well.
(f) PERUSH HA'MISHNAH L'HA'RAMBAM - The commentary that is printed in our volumes of Shas is a translation (from Arabic to Hebrew) of the first edition (Mahadura Kama) of the Rambam's commentary on Mishnayos, which he wrote at a young age. After the Rambam completed writing the Mishneh Torah, he re-edited the original draft of his Perush (that he had written in Arabic). One of his aims in doing so was to ensure that everything in the commentary was consistent with his rulings in the Mishneh Torah. This edited version is known as the Mahadura Basra ("final edition"). This final version was discovered and published in recent years by Rav Yosef Kapach.
[III] ACHRONIM
(a) At the end of the Vilna edition of the Mishnayos (in most offsets of this edition) can be found a commentary called "Ya'ir Kino." This is a remarkable commentary consisting of two parts. The first is based on the commentary of the Rosh on Kinim. The author explains and resolves all of the words of the Rosh in a clear and concise manner. The second is the commentary of the author himself on the Maseches, in which he examines all the words of the Rishonim and often proposes his own explanation for the Mishnah that emerges from his rigorous analysis of the Sugyos in Shas that deal with the Mishnah.
The author of Ya'ir Kino was Rav Menachem Eliezer from Vashilishak (near Vilna), son of the author of Ateres Rosh on Maseches Berachos, and a contemporary of the Vilna Ga'on. It is fitting to mention here what was written about this commentary in Sefer Aliyos Eliyahu (a biography of the Vilna Ga'on):
"When ha'Gaon Moreinu Menachem Eliezer, the son of the Ba'al Ateres Rosh, completed his Sefer on Maseches Kinim entitled Ya'ir Kino, he was still a very young man. He came with his Sefer before [the Vilna Ga'on] to show to him the Sefer. [The Vilna Ga'on] told him to leave the Sefer with him overnight. In the humility and greatness of the Gaon, and in his [pursuit of] truth, when he saw [that the author of the Sefer on Kinim] had approached with such clarity a difficult Masechta whose understanding had evaded many of the commentators, the Gaon learned the Sefer all night long. Early the next morning, the great [Rav Chaim of Volozhen] came to the place of learning of the Gaon. The Gaon said to him that a Sefer had been brought to him by a young man, the son of the Ateres Rosh, and that it was a most marvelous work on Kinim in which the author merited from Heaven to have revealed in many places the true understanding of the Maseches, which had not been revealed to any of the earlier commentators. [Rav Chaim] hurried to relate this to the author, and with much joy and confidence the author went to see the Gaon, expecting to be crowned by the Gaon with splendor and glory. But when he came before the Gaon, the Gaon handed his Sefer back to him and said not a single word about it." (Aliyos Eliyahu, p. 69)
(b) MAYANEI YEHOSHUA - a commentary printed in the Vilna edition of the Mishnayos, which was written by Rav Yehoshua Heller, author of the Mussar works, "Divrei Yehoshua" and "Chosen Yehoshua."
(c) KAN MEFURESHES - by the son of Rav Eliyahu Guttmacher of Greiditz (recently reprinted).
b'Hatzlachah in Maseches Kinim!