Gemara

Benei Baishan were stringent not to go from Tzur to Tzidon on Erev Shabbos (the market day). The next generation asked 'must we must follow this stringency? Our ancestors could be stringent. We cannot!'

(R. Yochanan): Since your ancestors accepted this, you must follow it - "Shema Beni Musar Avicha v'Al Titosh Toras Imecha."

Eruvin 36a (Mishnah): One may place one Eruv in the east, and one in the west and stipulate... If Chachamim come from both directions, I will go where I want.

R. Yehudah says, if one of the Chachamim is his Rebbi, he may go [only] in that direction.

Chachamim disagree, for sometimes a person prefers his friend over his Rebbi.

82a (Rav Yosef): One may be Me'arev only in order to [go to] do a Mitzvah.

Kidushin 30b (Beraisa): One must teach his son a trade.

(Chizkiyah): We learn from "see life with the woman whom you love";

Whether 'woman' literally means a wife, or, it alludes to Torah, just like it is a Mitzvah to take a wife for one's son or to teach him Torah, it is also a Mitzvah to teach him a livelihood.

Bava Metzi'a 30b (Rav Yosef): "V'Hodata Lahem [ha'Derech...]" refers to learning a trade (some explain - Torah).

Rishonim

Rif and Rosh (Shabbos 7b and 1:38): The Isur to embark less than three days before Shabbos is due to Bitul Oneg Shabbos. We permit due to a Mitzvah, since one engaged in a Mitzvah or on the way to a Mitzvah is exempt from other Mitzvos, e.g. Sukah (Sukah 25a).

Rambam (Hilchos Shabbos 30:13): For a Mitzvah one may embark even on Erev Shabbos.

Magid Mishneh: Nowadays the custom is to embark even to the Yam ha'Gadol on Erev Shabbos and Shabbos. The Ramban sought to defend this, but said that a Ba'al Nefesh should be stringent for himself. Also the Rashba said that his words [to defend the custom] are wrong.

Mordechai (Eruvin 257): One may go on a boat on Erev Shabbos for a Devar Mitzvah. R. Tam says that seemingly, business is a Devar Mitzvah. We say that "Re'eh Chayim" refers to a trade, and "v'Hodata Lahem [Es ha'Derech...]" refers to Beis Chayeihem. (Maharam says that this is a trade.) Also going to see a friend is considered a Devar Mitzvah. Going for Tiyul is Reshus.

Beis Yosef (OC 248 DH v'Havi): Perhaps we can say that everything is considered a Devar Mitzvah according to R. Tam. However, it seems that the Poskim disagree. Where the custom is to permit, we do not protest against them, for they have whom to rely on.

Rashi (Bava Metzi'a 30b DH Zeh): "Beis Chayeihem" is teaching [to one's children] a trade to finance themselves.

Ritva (Eruvin 45a DH umid'Rebbi): Returning from a Devar Mitzvah is [a Mitzvah,] just like going.

Poskim

Shulchan Aruch (OC 248:4): Three days before Shabbos, one may not go in a caravan if it is known that they will need to be Mechalel Shabbos due to danger. If one goes to [live in] Eretz Yisrael, even if the caravan leaves on Erev Shabbos, it is permitted, for it is a Devar Mitzvah.

Magen Avraham (15): This is only if he goes to settle in Eretz Yisrael. Some permit even if he intends to return to Chutz la'Aretz, for even walking four Amos in Eretz Yisrael is a Mitzvah.

Mishnah Berurah (28): Especially since the Rema is lenient below, we can consider going with intent to return to be a Mitzvah.

Kaf ha'Chayim (45): Eliyahu Rabah says that also the first opinion agrees that alighting to Eretz Yisrael [even without intent to settle there] is a Mitzvah. Pesach ha'Dvir says that Poskim argue about this. The Rambam holds that it is a Mitzvah, for he says that one who walks four Amos in Eretz Yisrael is guaranteed to be a Ben Olam ha'Ba. Some Acharonim say that settling in Eretz Yisrael is a Mitzvah mid'Rabanan. The Ramban says that it is an Aseh. The Sifri says that it is equal to all the Mitzvos, even after the Churban. The Chasam Sofer (233,234) says that Tzefas is greater than other cities of Eretz Yisrael, and Yerushalayim is greater than Tzefas.

Shulchan Aruch (ibid.): If one entered a city on Shabbos, he may walk in the entire city.

Magen Avraham (17): This is only if he went for a Mitzvah, but not if he went for business.

Rema: Some say that anywhere one goes for business or to see a friend is considered a Devar Mitzvah. Only going for Tiyul is Reshus. This is why the custom is in some places to embark on a boat or caravan within three days of Shabbos, because everything is considered a Devar Mitzvah. We do not protest against them, for he has whom to rely on.

Beis Yosef (DH u'Mah she'Chasav Rabeinu d'Lir'os): The Tur and Mordechai say that seeing a friend is considered a Devar Mitzvah. Not all Poskim agree with R. Tam [that business is a Devar Mitzvah]. If they did, why did they seek reasons to justify the custom to embark on Erev Shabbos? It should suffice that all go for business or to see friends, and not for Tiyul! The Rif and Rosh connote like this. They permit because one engaged in a Mitzvah is exempt from another Mitzvah (Oneg Shabbos). If going for business is a Mitzvah, the entire world is exempt from Mitzvos! Rather, surely they argue with R. Tam. The episode with Benei Baishan connotes like this. They were not going for Tiyul. They said 'we cannot be stringent'! If business is a Mitzvah, why were their ancestors stringent? It is not Midas Chasidus to be stringent [and refrain] from a Mitzvah! The Rivash (101) says that what the Tur brings form R. Tam is an excessive leniency. However, going to [live in] Eretz Yisrael is a Mitzvah. Tashbatz (1:21) says so.

Taz (5): Why is this different than 444:7? If one has Chametz in his house, only going to circumcise his son [or similar matters] are considered Mitzvos [to permit relying on Bitul. If one is going to other matters, he must return to destroy the Chametz - Pesachim 49a.]

Suggestion: Since embarking on Erev Shabbos is only an Isur mid'Rabanan, we are more lenient.

Rejection (Taz): Also there, if one is Mevatel Chametz, there is only an Isur mid'Rabanan [to leave it in the house]! We must say that the stringency of Chametz is different. One must refrain more from Chametz, since one is used to [eating] it. Therefore, one must return unless he is going to a great Mitzvah.

Magen Avraham (19): This is even if he has food, and he goes on business to profit. See 531:4. (One who returned from Chutz la'Aretz during the Mo'ed may shave, unless he left for Tiyul.) To collect money that a sick Nochri owes to him, unless he is Goses (probably going to die), this is not called a Vadai loss.

Gra (DH li'Schorah): This is even if he goes for profit, like Chachamim [of R. Yehudah - Mo'ed Katan 14a].

Mishnah Berurah (34): Eliyahu Rabah is lenient [to collect a debt]. It is no worse than going for business. Therefore, one may embark within three days of Shabbos for this. See Magen Avraham 339:13, Mishnah Berurah 339:36 (below).

Gra (DH Oh): We learn from Eruvin 36b [that one may make an Eruv in order to see his friend] and 82a (one may be Me'arev only for a Mitzvah).

Magen Avraham (19): The custom is to embark even on Shabbos. Mishpat Tzedek says that that one should not be lenient against the majority of Poskim. All the more so, if the boat goes for him, all forbid.

Magen Avraham (20): I say that one should not be lenient about a caravan.

Kaf ha'Chayim (42): We are lenient only for a boat, for it is a Safek whether he will need to be Mechalel Shabbos. In a caravan, he will surely need to be Mechalel Shabbos.

Kaf ha'Chayim (56): Perhaps the Magen Avraham permits to go in a boat and forfeit Oneg Shabbos, but not if he will leave the Techum. However, perhaps we are more lenient about the Techum, for in the sea there is no Techum mid'Oraisa, so one may rely on the Rema.

Chavos Ya'ir (115): Maharil said that praying in a Minyan is not such a Mitzvah for which one may be Me'arev. "V'Nikdashti b'Soch Bnei Yisrael", Kaddish, Amen Yehei Shmei Raba... are great Mitzvos, but they are not so incumbent on an individual. R. Gamliel freed a slave to make a Minyan, for if not, there would not have been a Minyan. One may not learn from one Heter for the sake of a Mitzvah to permit elsewhere. I forbid going in a boat to complete a Minyan, even though many Mitzvos will be Batel. We find that one may not leave the Techum to enable Teki'as Shofar. Even though it is permitted through a Nochri, a boat that goes just for him is different. We find that one who sits in a wagon [drawn by Kil'ai Behemah] is lashed!

Sha'arei Teshuvah (16): Chavos Ya'ir connotes that it is more lenient when the boat is not only for him, but in any case he forbids. He permits a ferry. It is not confused with a boat. Avodas ha'Gershoni (123) permits a doctor [to cross the river] only for one who is dangerously sick, or if the governor summonsed him, for Darchei Shalom. Nesiv Chayim (brought in Friedman Shulchan Aruch, Otzar ha'Poskim 11) permits going in a boat for a Mitzvah. One should be in the boat all of Bein ha'Shemashos to acquire Shevisah according to all opinions. Birkei Yosef 339:9 says that many are stringent, so one should rely on this only for a great need. All the Heterim are only within the Techum.

Kaf ha'Chayim (53): One may not leave on Shabbos or Yom Tov, or even Yom Tov Sheni.

Mishnah Berurah (36): Where there is no custom to be lenient, one should not be lenient l'Chatchilah, for many Poskim require an absolute Mitzvah.

Magen Avraham (339:13): A Nochri, who owed a great debt to Reuven, was sick. Reuven may not hire a boat to go to him, for there is no Vadai loss. Perhaps he will not die, or perhaps he will command his heirs to pay (Ri ha'Levi). This implies that one may go in a boat for a Vadai loss, e.g. bandits. See 334:17. (Some are lenient about saving money from a fire or bandits.) I say that a boat is more stringent. We do not permit it even for a Mitzvah! See 613:6. (One may walk through water on Yom Kipur for a Mitzvah, but he may not go in a boat.)

Mishnah Berurah (36): Chayei Adam says that if the only way to do a Mitzvah or save a large debt is if he goes on a boat, perhaps one may be lenient, unless he must leave the Techum.