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As we move to perek 2 of Yevamot, there are 5 new concepts that we will encounter. As I said in the previous installment, many of the specific examples that the Mishnayot introduce literally require a pencil and paper to sketch out, something that you may or may not have the time to do. But the basic concepts are not that hard to get (I think :). Your feedback is helpful here, as I want to be writing things that are useful to you.
The first concept is that of "the brother who was not in the world" (Mishnayot 1 and 2) . The basic idea is that the mitzva of "yibbum" does not apply to a brother who is born after the death of the childless brother. This "brother who was not [yet] in the world" is forbidden to marry his late, childless brother's wife, for she is simply categorized as "thy brother's wife". In addition, this late-born brother may not perform "yibbum" with a woman who was a co-wife of the childless brother's wife, such as in the case the case in which an already-married older brother had in fact perform "yibbum", and then also died childless.
The second concept (Mishnayot 3 - 4) is that there is a distinction drawn between instances in which a brother may not perform "yibbum" because his late brother's wife falls into the Torah's category of "incest" (as discussed in perek 1), and when the late brother's wife is forbidden either by rabbinic law (i.e. the Torah-law prohibitions expanded out one generation, e.g. from mother to grandmother), or if she is forbidden not as a matter of "incest" law, but as a violation of "holiness boundaries", e.g. a Kohen and a woman who had been divorced. In the latter categories the mitzva of "yibbum" still technically applies, but by rabbinic law "chalitzah" (the release ceremony) should be performed instead.
The third concept (Mishna 5) is that even a child who is (tragically) defined as a "mamzer" halachikly, is nonetheless recognized as being a man's child for all halachik purposes.
The fourth concept (Mishnayot 6-7) - and these Mishnayot are the hardest to drill down into - is that in addition to the the prohibition upon a man to marry his wife's sister, he is also prohibited to marry the sister of a woman with whom he had previously performed the "chalitzah"(release) ceremony. So in the interesting (if rather unlikely) scenarios described in these Mishnayot, "yibbum" is ruled out because the man may have previously performed a valid "chalitzah" with the woman's sister.
And finally (Mishnayot 8-10), there is deep rabbinic concern over situations in which a man, functioning as a witness or as a judge, contributes to the legal dissolution of a woman's marriage, and then goes ahead and himself marries that woman. Sure look suspicious, and the Sages prohibit any such marriages.
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