For whom may one transgress Shabbos
Extinguishing a lethal fire :
Any life threatening situation overrides [the] Shabbos [prohibitions], and whoever is quick [to transgress in order to save a life] is praised.
Children or sick people are endangered: Even if a fire ignited in a different courtyard and one is worried that it may spread into one’s own courtyard and it will pose danger, such as for example if there is a sick person or children [in his courtyard] and there is no time [for them] to run away before it will reach [them], then one is to extinguish [the fire] to prevent it from spreading.
It is possible to carry them out: Even if it is possible to escape [by carrying the children and ill person] through a Biblically considered public domain, then it is [still] better to extinguish [the fire, rather than escape].
The reason for this is: because extinguishing [a fire] is an action which is not done for its own use [and is thus only Rabbinically forbidden] as mentioned in chapter 278 [Halacha 1], while carrying out a sick person or children which are not able to walk is a Biblical prohibition as explained in chapter 308 [Halacha 81].
Removing an unknown person from danger on Shabbos:
We do not follow after the majority [of a population’s ethnic group] by a life threatening situation [as will be explained].
A mound fell in an area that a Jew was definitely around: It goes without saying that if there nine gentiles and one Jew standing in a courtyard and a building fell on one of them in that courtyard, and it is not known if it was a Jew [upon whom it fell] or a gentile, that one may undo the mound.
The reason for this is: being that the Jew and the gentiles were set in that courtyard and anything which is set is considered [a ratio of] half and half [even though in truth there is less than half of it] and in a case of doubt regarding if there is a life threatening situation [to a Jew] we rule leniently.
If one person separated from the group: [Furthermore] even if one person left to a different courtyard and [in that courtyard] a building fell on him in which case it is appropriate to follow the majority [of people, and thus not allow to remove the mound on Shabbos], even so we clear [the rubble] from on top of him.
The Reason: As since the original establishment [of 50:50] has remained in its state (at the time [that the person] left the [50:50] establishment) we therefore consider [this person who separated] as if he were still established with them to be lenient in a life threatening situation.
If the entire group left one after the other: However if the [entire] group uprooted from [their original place of establishment] one after the other, and at the time of the uprooting one of the group members left to a different courtyard and there a building fell on him, then one may not uncover it for him.
The reason for this restriction is: as since the original [50/50] establishment has already moved from its place (when this person separated from them) it is thus impossible to be lenient in it due to the concept of a [50/50] establishment and we [thus] go after the majority of which were gentiles.
If the entire group left together: However if the entire group left together, then they are still considered established together and when one person separates from them, he has separated from a [50/50] establishment and one is to undo the mound from on top of him.
An abandon baby in a city of majority gentile population: Likewise an [abandoned] baby which was found in a city that is majority gentile, there are opinions which say that one may not desecrate Shabbos for him, as since every day everyone separates from their established area we therefore go after the majority (as is explained in Even Haezer Chapter 4 [Halacha 34], [although] see there for opinions which argue).
If there are many doubts involved in the case:
One which fell upon him a mound and there is doubt as to whether he is still alive or already dead, [and] a doubt if he is under there or he is not under there, and even if one were to say that he is under there is doubt as to whether he is a Jew or a gentile, one is to undo the mound from upon him even though there are many doubts involved.
The reason for this is: because the Torah says “you should live by them” that it cannot be made to lead under any circumstances towards the death of a Jew through keeping the Mitzvahs.
Saving a life even only momentarily:
Even if [the victim] was found to be crushed and is thus is only able to live momentarily, [nevertheless] one is to undo the mound up to his nose and check him [for if he still has life] and if he is still alive then one is to undo the mound and take him out for him to live whatever amount longer [that doing so will allow him to live]. [However] if one did not feel life in his nose, then he has certainly already dead even if he was not crushed.
Checking if the person is already dead:
Whether [the victim] got hit first on his head or first on his feet and one sees that there is no life in his heart, even so one is to check up to his nose, as the main evidence of whether there is life is in the nose, as it says [in the verse] “all that have a soul of life in their nose”.
If the upper part of the mound had dead people found in it:
If one found the upper [bodies in the mound] to be dead one does not assume that the lower ones have already also died and rather is to undo the mound from on top of them as perhaps they are still alive.
There was an incident [which proves this point as a mound fell and the searchers found] the top ones to be dead and the bottom ones were found alive.
Saving a robber from death on Shabbos:
One who comes through a tunnel [to rob a house] in a scenario that [the robber] has given up his blood and it is permitted [for the homeowner] to kill him [in self defense], and a mound fell on him there [in the tunnel] one may not undo it for him (as one is not commanded to help him live).
Fighting battle against gentiles on Shabbos:
For monetary purposes: Gentiles which have sieged a city of Jews, if they have come to for monetary purposes [to loot the town] then one may not desecrate Shabbos.
To defend lives: However if they have come to kill the inhabitants, even if they have come as they do typically but there is worry that perhaps they have come to kill, and even if they have still not yet come but they are preparing to come, then the town may go out to greet them with weapons and they may desecrate Shabbos on their behalf [to defend themselves].
A border town: A city that rests near the border, then even if the gentiles only want to come for purposes of [taking] hay and straw, one is to desecrate Shabbos as [otherwise] perhaps the city will be conquered [by the gentiles] and from there it will be easy to conquer the remainder of the land.
Other Opinions: There are opinions which say that in these days that we live between non-Jews which loot and kill, then even if they have only come [to steal] money, [nevertheless] one is to desecrate Shabbos due to them.
The reason for this is: because if the Jew will not allow the robbers to steal and loot then they will kill the Jew, and it is presumable that a person does not stand by and allow his money to be taken and there is thus worry that perhaps one person will stand up against the robbers and they will kill him, and this is thus a situation of life and death.
The Final Ruling: Nevertheless it all depends on the situation.
However robbers came upon a single person to rob his money, then he is to let them take everything he has and may not desecrate Shabbos even to do a Rabbinical prohibition, with exception to ways explained in chapter 301 [Halacha 38].
Helping save another Jew:
When there is no danger involved for the rescuer: One who sees a ship, which contains Jews, drowning in the sea, as well as [one who sees] a river that is drowning [another person], as well as [one who sees] a Jew being chased by a gentile then it is a commandment upon every individual to desecrate Shabbos in order to save them, even if there is doubt as to whether they will be saved.
When there is danger involved for the rescuer: Nevertheless if there is danger [involved in trying to save the Jew] one may not endanger himself in order to save his friend because [in the mean time] he is not within the range of danger. [This applies] even if one is witnessing the death of his friend and even if his danger [in trying to save him] is doubtful while his friend’s is certain, nevertheless [he is not to put himself in danger to save him]. [However see supplement that this is only in accordance to one opinion].
The reason for this is: as the verse states “You shall live by them” and not that one should come into doubt of death through fulfilling the Mitzvah of “Do not stand by the blood of your friend”.
Supplement from Choshen Mishpat Hilchos Nizkeiy Haguf Vehanefesh Halacha 7:
One who sees a friend drowning in the sea or that murderers are coming upon him and he is able to personally save him or to hire someone to help save him, then he is obligated to trouble himself to hire others to save him, and he then returns and collects the money from the victim if the victim has the money, and if not then he may not refrain from [paying to help save him], and if he does refrain from doing so then he transgresses the command of “do not idle while your friends blood is being spilled”.
When there is danger involved for the rescuer: Even to enter oneself into a questionable case of danger one must do in order to help save his friend from definite death. (However there are opinions which argue on this, and Safek Nefashos Lehakel).
Returning home with the weapons:
Whoever is going out to save may return with their weapons to their towns if they fear from the gentiles to remain in the area of conquest as is explain in chapter 407 [Halacha 3].
Saving a Jew from forcibly giving up his religion:
One who gentiles are trying to force to give up his religion regarding whether one may desecrate Shabbos to save him was explained in the end of chapter 306 [the last Halacha].
 The Michaber there rules like the Rambam, that if majority of the town are gentiles then one may not remove a mound from an Asufi on Shabbos.
 The Rama there rules that even if the majority of the population are gentiles one may still desecrate Shabbos to save the Asufis life, as we view the Jews in the city as Kavua and thus is 50/50.