Rambam - 1 Chapter a Day

See the notes on Chapter 2, Halachah 7.

I.e., which is in his possession at that time.

Although ultimately this money will accrue to the estate, since it is not in the father’s possession at the time of his death, the firstborn does not receive a double share.
The Rambam’s statements regarding a loan are taken from Bava Batra 125b. If, however, security was given for the loan, the firstborn receives a double portion (Maggid Mishneh). See also Halachah 5 and see Hilchot Malveh V’Loveh 7:4.
The Ra’avad explains that the Rambam’s statements about a ship at sea are derived from Arachin 17b. There, the Mishnah is speaking about an instance when a person was obligated to bring a sacrifice whose value is linked to his financial status. The Mishnah states that even though a person possesses a ship that is at sea, the assessment for the sacrifice is made according to his immediate financial standing, and at that time he has no resources. Similarly, in this instance, the ship is not considered to be money within the estate at present, but money that will accrue to it later.
The Maggid Mishneh questions the Rambam’s ruling and the Ra’avad’s explanation, noting that the Talmud (and the Rambam in his Commentary on the Mishnah) interpret the situation as referring to an instance where the ship was hired out to another person. The Talmud is explaining that the person is still considered poor, because the rental fee for the ship is not due until the conclusion of the rental period. And he is not considered to be wealthy because of the ship himself, because when we calculate a person’s assets we do not include the property he uses to earn his livelihood.
The Maggid Mishneh points out: a) In Hilchot Arachin 3:18, the Rambam rules that a ship is not considered in the category of the tools to earn a livelihood that are excluded when calculating a person’s assets; b) in this instance, the person is deceased and we are no longer concerned with his earning his livelihood, the ship (and any merchandise belonging to him on it) is seemingly part of his estate. The Rashba also rules in this manner. This appears to be the opinion of the Shulchan Aruch (Choshen Mishpat 278:3). For when mentioning the concept that a firstborn does not receive a double share of a loan, the entire issue of a ship is not discussed.
The Rambam La’Am gives a practical explanation of the Rambam’s ruling. Because of the dangers (both of sinking at sea and being raided by pirates) inherent in a ship’s voyage, it and its contents cannot be considered money possessed by the estate.

For a fixed fee.

For a share of the profits.

After the father’s death.

If its weight increased and it was sold (Sefer Me’irat Einayim 278:5).

The rationale is that although the increase in the value of the cow and the calf itself were not in the possession of the estate at the time of the father's death, they are considered as coming about as a matter of course, like a tree that grows larger. (See Halachah 4.) Hence, it is as if they were originally part of the estate.
The Ra’avad maintains that the Rambam’s opinion regarding the calf represents a minority opinion in Bava Batra 124a, and it should not be accepted as halachah. The Maggid Mishneh interprets that Talmudic passage differently and maintains that the opinion on which the Rambam’s ruling is based is accepted by the majority of the Sages.
The Maggid Mishneh compares this halachah to Halachah 4 and raises a difficulty: Halachah 4 states that the firstborn does not receive a double share of grain and dates, even though the produce had already began to grow when he inherited the estate, because the growth and ripening of the produce is considered a change. Seemingly, the birth of the calf represents an even greater change.
The Maggid Mishneh offers - albeit with reservation - a possible resolution based on our Sages’ principle (Yevamot 78a, et al): “A fetus is like the thigh of its mother.” Thus, it is as if it has not changed. Ketzot HaChoshen 278:3, however, reinforces this conception, citing Avodah Zarah 47a, which states that “the fetus was originally an animal and now it is an animal, only then the gateway to its mother’s womb was closed.”
Ketzot HaChoshen also cites another ruling of the Rambam (Hilchot Geneivah 1:11), which expresses the same principle: “When a stolen article increases in value while it is in the thief’s possession - e.g., a sheep bore a lamb... - [the thief] must return the sheep... and its offspring.” Although a thief need not return an article that undergoes a fundamental change, the birth of the lamb is not considered such a change.
The Ra’avad and the Tur differ with that ruling. Similarly, in this instance, the Tur maintains that the firstborn does not receive a double portion of the offspring. The Rambam’s opinion is quoted by the Shulchan Aruch (Choshen Mishpat 278:4), while the Ramah cites that of the Tur.

This law would not apply if the animal was slaughtered after the person’s death.

As Deuteronomy 18:3 states, whenever a person slaughters an ordinary animal (in contrast to a sacrificial animal), he is required to give a priest the animal's foreleg, jaw, and maw as presents. The father who died was a priest and because of their bonds of friendship, the person slaughtering the animal would always give the presents from the animals he slaughtered to him. Even if the presents were not separated from the animal at the time of the father’s death, he is considered to have acquired them during his lifetime. Hence, they are considered to be part of the estate rather than a later increment, and the firstborn receives a double portion (Bava Batra 123b).

He cannot be compelled to give his brother a portion of the land.

The rationale is that this increase was not part of the estate at the time of the father’s death.

In its initial state, the kernels were not formed, and then they became formed. In Hebrew, the names of the grain in the two stages are different. Hence, the entity is considered to have undergone a change.

In both these instances, the name of the entity remains the same.

Sefer Me’irat Einayim 278:13 emphasizes that this applies even when the investment was made with money from the estate.
The Ramah (Choshen Mishpat 278:6) states that if the firstborn protested and told his brothers not to make the investment until the estate was divided, he is given a double portion of the increase in value.

Since the debt was paid with land and from the time the promissory note was composed, the land was on lien to the debt, there is room to consider the land as being part of the estate at the time of the father’s death. In such an instance, the firstborn would deserve a double share. Hence, the Rambam feels it necessary to mention that he does not.
As mentioned in the notes above, even if the father was given land as security for the loan, as long as the debtor has the right to redeem the land, it is not considered to be part of the estate, and the firstborn should not be given a double portion from it (Hike hot Malveh V’Loveh 7:4).

And we assume he made the decision to - and in his mind, actually transferred the money - so that it would be part of his father’s estate at the time of his death, in order to receive his double portion from it (Sefer Me’irat Einayim 278:18).

Sefer Me’irat Einayim 278:19 states that this is an exception to the general rule: “Whenever a person desires to expropriate money from a colleague, the burden of proof is upon him.” Here also, there is room to think that the other brothers would not be able to expropriate the extra share from the firstborn. This rule, however, is not applied in this instance.

I.e., because his portion is distinct, if he waives it, the waiver is binding and he is considered to have forfeited his right. If, however, it were not distinct, the waiver could not be binding until the estate was divided and the extra share set aside.
There is a difference of opinion among the Sages of the Talmud that has been perpetuated among the later authorities whether an ordinary son can sell his share (or the firstborn can sell his ordinary share) before the estate is divided. Some maintain that just as a partner can sell his share of a business before the resources of the partnership are divided; so, too, an heir can sell his share of the estate. Others maintain that a portion of an estate does not exist until it is actually allotted. Hence, it cannot be sold.

I.e., he need not express his consent. The fact that he remains silent is considered to be acquiescence [Ramah (Choshen Mishpat 278:9)].

For the wine is considered to be a distinct and different entity. Hence, he is required to issue a new protest.
The Ra’avad and the Rashbam interpret Bava Batra 126a, the source for the Rambam’s ruling, differently. The Maggid Mishneh writes that both interpretations are acceptable.

As Deuteronomy, Chapter 25, relates when a man dies childless, his brothers are commanded to marry his wife. See Hilchot Yibbum VaChalitzah, where this rite is described at length.

Even if the deceased brother’s father is alive, the brother who marries the widow acquires his estate. Ordinarily, the father would have a prior claim, but his rights are superseded because of the marriage (Yevamot 40a).

Yevamot 24b does not follow the literal meaning of the verse and interprets it to mean that the deceased brother’s inheritance is given to the brother who marries his wife. He is the “firstborn” to whom the verse - in its halachic meaning - refers. Accordingly, the same restrictions that apply with regard to the manner in which a firstborn inherits his father’s estate, apply with regard to this brother’s inheritance of his brother’s estate.

I.e., here too, the laws that apply to a firstborn’s inheritance apply to his. See the statements of the Ramah Even HaEzer 163:1), which quotes different opinions as to whether the equivalence is exact or not.

He does acquire the entire increase in the property contained in his brother’s estate - even the increase that occurs before he marries his brother’s widow (Maggid Mishneh).

As the Rambam states at the conclusion of the halachah, we are speaking about a situation in which a father had several sons. The father died and then one of the sons died without leaving any children, and one of the brothers married his widow. That brother receives two shares in his father’s estate, his own share and the share of the deceased.
If, however, the brother who died childless had died before his father, the brother marrying his widow would not receive an extra share in the father’s estate. For that share was “fit to be acquired” only by the deceased brother. As stated above, the brother marrying the widow does not receive an extra share of property fit to be acquired.

At which time he acquired his brother’s property.

Chapter 12, Halachah 12.
This is derived from the exegesis of Deuteronomy 21:18. In his gloss on Hilchot Shechenim, the Maggid Mishneh (and Sefer Me’irat Einayim 174:11) state that this law applies even if the entire property is not of uniform value, and one share is not the same size as the others. For if this were not so, and the ruling were to apply only with regard to shares of equal value, there would be no need for a verse. Instead, the law would be obvious from Halachah 1 of that chapter in Hilchot Shechenim, which states that when brothers come to divide a field that is all of uniform value, without one place being better and another worse, and one says: “Give me my portion on this side so that it will be close to another field that I own, so that they will be one large field,” his request is heeded. “Holding back in such a situation would be [a reflection of] the traits of Sodom.” Following the same logic, if the portions of the field were all of equal value, there would be no reason not to give a person who marries his brother’s widow both of his shares together. Indeed, not to do so would be emulating the traits of Sodom.

I.e., the double portions he receives are an integral entity and not a combination of two portions.

As Rashi explains in his commentary on Bava Batra 12b - the source for this halachah - since the two portions come from inherently separate rights, there is no obligation to join them together.

As explained in Hilchot Yibbum VaChalitzah 2:1, although according to Scriptural Law, the brother of the deceased acquires the deceased's childless wife through marital relations alone, before engaging in relations, it is preferable that he designate her as his wife by giving her money. The act of designating her as his wife is referred to as ma'amar.

As explained in Hilchot Ishut, Chapter 16, the term nichsei m'log refers to property a woman brings to her household that the husband is allowed to use until it is worthless. In the event of his death or the couple's divorce, the property is returned to the woman as is.

As explained (ibid.), the term nichsei tzon barzel refers to property a woman brings to her household for which the husband accepts financial responsibility. It is evaluated at the outset, and a financial equivalent is established. In the event of his death or the couple's divorce, that sum must be paid to the woman.

As explained in Hilchot Ishut, Chapter 12, a husband obligates himself to pay his wife a minimum of 100 or 200 zuz in the event of his death or the couple’s divorce. Moreover, it was customary for an additional sum to be appended, depending on the couple’s financial standing.

Since the husband’s brothers were obligated to marry her, there is room to say that the woman’s financial connection to her deceased husband has not been severed, and hence, his heirs have a right to her estate. On the other hand, since they did not marry her before she died, and her husband already died, her heirs also have room to claim her estate. Our Sages did not resolve whose claim is stronger, but instead ruled to divide the estate between the two sets of heirs.
The rationale for the division suggested can be explained as follows: The nichsei m’log are considered to be in the woman’s possession. Therefore, her family’s heirs acquire them. The money due her by virtue of her ketubah is not due the woman in her husband’s lifetime. Hence, it is considered to be in the possession of the husband’s heirs and is therefore retained by them. And the status of the nichsei tzon barzel is a matter of question; hence they are divided.
The Shulchu. it Aruch (Even HaEzer 160:7) quotes this view. The Ramah quotes other opinions, which maintain that the husband’s heirs are able to maintain possession of the nichsei tzon barzel entirely.

Hilchot Ishut 12:4.