Gemara

(Mishnah): If one did not bring Chagigah the entire Regel, he is not obligated to bring it afterwards. About this it says "Me'uvas Lo Yuchal Liskon v'Chesron Lo Yuchal Lehimanos".

Objection (Bar Hei Hei): About such an omission it should say 'Lehimal'os', not "Lehimanos"!

(Bar Hei Hei): Rather, "v'Chesron Lo Yuchal Lehimanos" refers to one who was not counted with his colleagues for a Mitzvah.

Support (Beraisa): "Me'uvas Lo Yuchal Liskon" refers to one who missed Kri'as Shma or Tefilah in the morning or evening; "v'Chesron Lo Yuchal Lehimanos" refers to one who was not counted with his colleagues for a Mitzvah.

Berachos 26a (R. Yochanan): If one mistakenly omitted Ma'ariv, he prays Shacharis twice. If he mistakenly omitted Shacharis, he prays Minchah twice.

Question: If one mistakenly omitted Minchah, does he pray Ma'ariv twice?

If one omitted Ma'ariv, he prays Shacharis twice because the Tashlumim (compensation) is during the same (Halachic) day - "Va'Yhi Erev va'Yhi Voker Yom Echad" (here, the Tashlumim would be the next day);

Tefilos are in place of Korbanos. If a Korban (with a fixed time) was not brought that day, there is no Tashlumim;

Or, since Tefilah is a request for mercy, one may pray at any time!

Answer (R. Yochanan): If one mistakenly omitted Minchah, he prays Ma'ariv twice. We do not equate this to a Korban, which may not be offered on a later day.

Question (Beraisa): "Me'uvas Lo Yuchal Liskon" refers to one who missed Kri'as Shma or Tefilah in the evening or morning. (There is no Tashlumim even on the same day, all the more so there is no Tashlumim for Minchah the next day!)

Answer (R. Yitzchak): The Beraisa discusses one who intentionally omitted Tefilah. (It teaches that even Ma'ariv and Shacharis, which have Tashlumim on the same day if they were omitted b'Shogeg, have no Tashlumim if omitted b'Mezid.)

Support (Rav Ashi): The Beraisa says 'omitted', it does not say 'mistakenly.'

Rishonim

The Rif and Rosh (Berachos 18a and 4:2) bring the Gemara in Berachos.

Question: Why must one compensate for omitting Ma'ariv? We hold that it is Reshus (optional)!

Answer #1 (Rif 19a and R. Yonah 18a DH Gemara citing BaHaG): When one prays Ma'ariv, he makes it obligatory on himself.

Answer #2 (Rif, R. Yonah and Rosh, ibid.): Even the opinion that says that it is Reshus agree that it is a Mitzvah, just it is not obligatory.

R. Yonah and Rosh: Even though it is Reshus, one should not neglect it without a pressing reason, e.g. a Mitzvah that cannot be done later, or if one already untied his belt and it would be an exertion to fasten it again. Yakov Avinu enacted Ma'ariv, and Chachamim taught that it corresponds to limbs and fats that may be offered at night. Just like they are not Me'akev Kaparah, Ma'ariv is a Mitzvah (that is not requisite).

Question: Rav taught that Ne'ilah on Yom Kipur exempts Ma'ariv (Yoma 87b). The Gemara asks, in any case Ma'ariv is Reshus! According to Answer #2, why is this difficult? One should not neglect it without reason!

Answer (R. Yonah and Rosh): There, there is a reason to omit it. He needs to prepare the meal for Motza'ei Yom Kipur, which is like a Yom Tov. Since he is tired from the fast and praying, we do not exert him.

R. Yonah: This question applies also to Answer #1, but the answer does not. Therefore, Answer #2 is primary.

Rambam (Hilchos Tefilah 3:8): If b'Mezid one did not pray a Tefilah in its time, there is no solution. He does not compensate afterwards. If he was Shogeg, Ones or distracted, he compensates for the missed Tefilah at the next time for Tefilah. First he prays the current Tefilah, and then the Tashlumim.

Rambam (9): If mistakenly one did not pray Shacharis before midday, he prays Minchah twice. The first Tefilah is Minchah, the second is Tashlumim for Shacharis. If mistakenly one did not pray Minchah before Shki'ah, he prays Ma'ariv twice. If mistakenly one did not pray Ma'ariv before dawn, he prays Shacharis twice.

Rambam (10): If mistakenly one did not pray a Tefilah in its time, nor the next Tefilah in its time, he compensates only for the latter. If mistakenly one did not pray Shacharis or Minchah, he prays Ma'ariv twice. The first Tefilah is Ma'ariv, the second is Tashlumim for Minchah. There is no Tashlumim for Shacharis, for its time has gone. The same applies to other Tefilos.

Ra'avad: This is an individual's opinion. He saw the Gemara mention Tashlumim at the next time for Tefilah. I will not permit or forbid. If one wants to compensate, he may. However, if one remembered during the time of the next Tefilah and did not compensate, he cannot do not so afterwards, for it is as if he omitted Tefilah b'Mezid. Also, it seems that Tashlumim is only with the current Tefilah, for it is the time of prayer.

R. Yonah (18a DH To'oh (1)): Some say that there is always compensation, and one who was sick or imprisoned compensates for all Tefilos that he missed. The primary opinion says that he can compensate only for one. However, he can pray Nedavah with (intent for) a new matter. It is proper to do so.

Rosh (ibid.): The Rashbam says that if one did not remember until the time for Minchah that he omitted Ma'ariv, he cannot compensate, since two times for Tefilah have passed. The Gemara did not ask about Tashlumim for Musaf. Since we mention Korban Musaf in the Tefilah, it is fitting only when Musaf can be offered. Even though the other Tefilos were enacted corresponding to Korbanos, they do not mention the Korbanos. They are requests for mercy. It would be great if a person prayed the entire day! Compensation is only if one erred, not for Mezid. A Gaon writes that if one missed a Tefilah, this is "Me'uvas Lo Yuchal Liskon". It is Reshus for him to pray an extra Tefilah. He gets reward for an optional request for mercy, but not for a Mitzvah.

Poskim

Shulchan Aruch (OC 108:1): If one did not pray Shacharis due to a mistake or Ones, he prays Minchah twice. The first Tefilah is Minchah and the second is Tashlumim.

Mishnah Berurah (1,2): If one did not pray because his mind was not settled or he was unable to wash, even though he should have prayed, this is not called Mezid and Tashlumim helps. If one was engaging in public needs he should pray Tashlumim like a Nedavah with a Chidush.

Mishnah Berurah (4): A Shali'ach Tzibur who repeats Shemoneh Esre is Yotzei Tashlumim. He should intend for his Tashlumim and also to be Motzi one who does not know how to pray.

Mishnah Berurah (5): One is not Yotzei by listening to the repetition of Shemoneh Esre, for this was enacted for one who does not know how to pray. However, if one listened to the repetition of Shacharis with intent to compensate for Ma'ariv, he was Yotzei. We are lenient about Ma'ariv because it is Reshus.

Shulchan Aruch (2): If one erred and did not pray Minchah, he prays Ma'ariv twice. The first Tefilah is Ma'ariv and the second is Tashlumim. If one erred and did not pray Ma'ariv, he prays Shacharis twice. The first Tefilah is Shacharis and the second is Tashlumim.

Mishnah Berurah (10): One may not eat before praying the Tashlumim for Ma'ariv. Some say that if he began he need not interrupt. It seems that he must interrupt, for one must pray the Tashlumim as close to the current Tefilah as possible.

Kaf ha'Chayim (11): Alfasi Zuta says that Tashlumim must be during the primary time for Tefilah, i.e. Shacharis until four hours of the day or Minchah until Plag ha'Minchah. Machazik Berachah says that it seems that the Poskim disagree.

Kaf ha'Chayim (17): If one needs to compensate and there is only time in the next time for prayer) for one Tefilah, he prays the current Tefilah and may pray a Nedavah later in place of the missed Tefilah.

Shulchan Aruch (3): One can compensate only at a time of Tefilah.

Beis Yosef (DH v'Chosav Od): The Gemara says that to compensate one prays Shacharis (or Minchah...) twice. It did not say that one may compensate the entire morning (or afternoon...). The Rashba infers that the Tashlumim must be together with the next Tefilah.

Mishnah Berurah (15): Some say that this is even b'Di'eved. Therefore, if one did not pray Tashlumim immediately after the current Tefilah he should intend that if it is not Tashlumim it is a Nedavah.

Shulchan Aruch (4): Compensation is only in the next Tefilah. If one erred and did not pray Shacharis or Minchah, he prays Ma'ariv twice. The latter is Tashlumim for Minchah. There is no Tashlumim for Shacharis. The same applies to other Tefilos.

Shulchan Aruch (5): Even though there is Tashlumim only at the next Tefilah, but not for other missed Tefilos, if he wants he can pray them for Nedavah with any Chidush. It is proper to do so.

Magen Avraham (8): The Rema (107:2) says that a Chidush must be a new need that arose after the previous Tefilah. If so, it is impossible to do so regarding Tashlumim which must be immediately after the previous Tefilah)!

Kaf ha'Chayim (26): Piskei Tosfos says that nowadays one should not pray Nedavah. We permit when there is a Safek whether or not one should pray again. Here this is not considered a Safek, for most say that there is Tashlumim only for the last period of prayer.