Marrying a Kohenes:
An Am Haaretz/Ignoramus is not to marry a Kohenes. If he does so, their marriage will not be successful, as either she or he will quickly die or they will be in constant fight with each other [or they will be poor]. However, a Sage who marries a Kohenes, [their marriage] is pleasant and praised, as the Torah and priesthood complement each other [and their marriage is a Segula for wealth]. [Some Poskim rule that this type of Am Haretz no longer exists today, as it refers to one who belittles and scorns at the Mitzvos, and is not measured by scholarliness. Others however rule that an Am Haretz includes anyone who is not Halachically defined as a Talmid Chacham. Nonetheless, today, one may be lenient in the definition of a Talmid Chacham, and so is the custom to marry a Kohenes.
The Chabad directive: The directive of the Tzemach Tzedek was for the Chasan to be well versed in one Misechta, in order to leave the status of an Am Haretz in this regard. The Chabad Rabbeim instructed that the Chasan is to study by heart one tractate of the Talmud and repeat it from memory each day. Elsewhere, the Tzemach Tzedek directed that the husband gives a small amount of money each day to charity, throughout his life. Thus, one has an alternative to learn daily, or give charity daily. The above is to be done without a Neder. Practically, the Rebbe negated the need for one to follow the above directives and give charity daily, or review the Tractate of Mishnayos daily, and rather suggested as follows. The Rebbe advised that the Chasan add in Torah learning. He is to be well versed in one Misechta before his wedding. One may choose any Tractate in the Talmud, even the small Tractates, such as Miseches Kallah. One is not required to memorize the text, but rather to know its content. On one occasion, the Rebbe directed the Chasan to study the entire Shisha Sidrei Mishneh prior to the wedding, or at the very least one or two Sedarim. On another occasion, the Rebbe directed that if possible, one is to be an expert in the laws written in Kitzur Shulchan Aruch.]
One who is not a Talmid Chacham is not to marry a Kohenes. The custom in today’s times is to be lenient in this matter, although prior to the wedding, the Chasan is to study and be well verses in at least one Tractate of the Talmud. It suffices to be well versed even in a small Misechta, such as Miseches Kallah. In general, the Chasan is to increase in Torah study.
 Pesachim ibid
 The source: This is learned from the verse [Vayikra 22] which states that if a Kohenes marries a Zar, and she becomes a widow, or divorcee, or has no children, from which we learn that a Kohenes is meant to marry a Kohen, and if she marries a Zar, then any of the above may occur. [Rav Chisda in Pesachim ibid]
Case examples: Rebbe Yehoshua married a Kohenes and became weak. He stated that seemingly Ahron is unhappy with him marrying one of his daughters. Rav Kehana blamed his exile and wandering on the fact he married a Kohenes. [Pesachim ibid]
 Pesachim ibid “Rebbe Yochanon said: One who desires wealth is to marry a descendant of Ahron. Rav Sheshes said in the name of Rav Papa that he became wealthy due to marrying a Kohenes.”
 Michaber ibid; Pesachim ibid; Rivash 15; Maharam 605; Tzemach Tzedek ibid
Other opinions: See Tzemach Tzedek ibid for a discussion of why the above Amoraim, who were certainly Talmidei Chachamim, nevertheless felt they were punished for marrying a Kohenes. He explains there that these Amoraim held that even a Talmid Chacham cannot marry a Kohenes, thus arguing on the conclusion of the Gemara ibid. See however Maharsha ibid that one can simply say that due to his humility, Rav Kahana did not view himself as a Torah scholar.
 Chavos Yair 70, brought in Pischeiy Teshuvah 2/9 and Y.D. 217; Aruch Hashulchan 2/5
 Tzemach Tzedek ibid; Maharam Shick 6 “In today’s times an exceptional Bachur who is G-d fearing person may marry”; Avnei Tzedek 5 that there is a middle level of one who is not a Talmid Chacham but also not an Am Haaretz;
 The reason: Although, in truth, having knowledge of one Misechta does not define one as a Talmid Chacham, nevertheless, since the Kohanim today do not have true proof of lineage, and thus cannot eat Biblical Teruma, as well as that many are anyways lenient in this matter, and Shomer Pesaim Hashem, it therefore suffices to study only one tractate. [Tzemach Tzedek ibid; Likkutei Sichos 19/509; Igros Kodesh 11/115; Avnei Tzedek 5]
 Tzemach Tzedek Even Haezer 11 “So long as he knows one Misechta”, mentioned in various responses of the Rebbe, brought in Igros Kodesh below.
 Maaneh of Rebbe Rashab to Rav Klotzkin, printed in Yagdil Torah N.Y. 20 Nissan 5738
 Response of Rebbe Rashab that so directed the Tzemahc Tzedek, printed in Yagdil Torah N.Y. 20 Nissan 5738, mentioned in Likkutei Sichos 19/509
 Response of Rebbe Rashab that so directed the Tzemach Tzedek, printed in Yagdil Torah N.Y. 20 Nissan 5738, mentioned in Likkutei Sichos 19/509
 Likkutei Sichos 19/509
The reason: As the custom today has become to be lenient in this matter, and Shomer Pesaim Hashem, and the more careful one is to negate any harm, itself emphasizes the harm. It thus suffices for one to be considered like a Talmid Chacham before the wedding , and he then no longer has to worry about this matter. [Likkutei Sichos 19/509]
 Igros Kodesh 5/283; 6/83; 7/154
 Likkutei Sichos 19/509; Igros Kodesh 5/283; 11/115; 13/123; 14/383
Marrying the granddaughter of a Kohen: On one exceptional occasion, the Rebbe directed one who married the granddaughter of a Kohen to be an expert in one Tractate. This was a personal directive, and is not a directive for the public. [Rishumo Shel Shana 5744, brought in Shulchan Menachem 6/249]
 Likkutei Sichos 19/509; Igros Kodesh 6/83; 14/383; Mikadesh Yisrael p. 215, brought in Shulchan Menachem 6/249
What is Miseches Kallah and where is it found? Miseches Kallah is part of a number of very small Tractates that are laws without commentary, and do not have on them the commentary of the Talmud. These Misechtos are found in the end of Seder Nezikin, after Tractate Horiyos. This Tractate contains one chapter, and should not be confused with Tractate Kallah Rabasi which is a later work.
 Igros Kodesh 13/123; 14/383; In one reply, the Rebbe directed the Chasan to learn the Tractate 40 times. [Mikadesh Yisrael p. 215, brought in Shulchan Menachem 6/249]
 Igros Kodesh 6/83; See also Shemuos Vesippurim for a simialr directive of the Rebbe Rashab to Harav Murozov, who married the daughter of a Kohen, that “This matter is not to be taken lightly, and he is to be an expert in Seder Kodshim.”
 Igros Kodesh 5/283