Shulchan Arukh, Orach Chayim 108/שולחן ערוך·אורח חיים ק״ח

1One Who Did Not Pray Due To A Mistake, Or An Extenuating Circumstance, Or On Purpose. Containing 12 S'ifimIf one erred or was forced [by circumstance] and did not pray the morning prayer, one should pray the afternoon prayer twice: the first is the afternoon prayer, and the second as a make-up. If one inverted [the order], one has not fulfilled one obligation in prayer for the prayer which is a make-up, and one needs to go back and pray it [again]. And the same law applies in every case in which one must pray a make-up prayer.

2If one erred and did not pray the afternoon prayer, one should pray the evening prayer twice: the first is for the evening prayer, and the second is for the make-up. If one erred and did not pray the evening prayer, one should pray the morning prayer (i.e. Amidah) twice: the first for the morning prayer, and the second as a make-up. After one says "Yotzeir" [the blessings of the Recitation of the Sh'ma in the morning prayer] and the Eighteen Blessings (i.e. the Amidah), one should say Ashrei and then afterwards pray the Eighteen Blessings for the make-up evening prayer. [And similarly, when one prays the evening prayer twice because one did not pray the afternoon prayer, one should say Ashrei between one prayer [i.e. Amidah] and [the other] prayer.] [Sefer Mitzvot Katan and the Rivash - Siman 140]

3[This statement] that one can complete [i.e. make-up] the [Amidah] prayer that one missed applies specifically during the time of [the next Amidah] prayer, but when it is not the time of [that next Amidah] prayer, one may not.

4There are no make-up prayers other than the immediately adjoining [i.e. preceding] prayer alone; so that if one erred and did not pray the morning prayer and [also] the afternoon prayer, one [only] prays the evening prayer twice [with] the latter prayer as a make-up for the afternoon prayer, but for the morning prayer there is no make-up; and the same goes for all the rest of the prayers.

5Even though there are no make-up prayers other than for the prayer immediately adjoining that prayer, and (other) prayers that one missed [i.e. one skipped two or more as mentioned above] do not have a make-up; if one wants to pray that one [i.e. the one that cannot be make-up anymore] as a voluntary prayer and one will innovate something [new] into it, one is allowed to and it is proper to do so.

6If the whole day passed and one did not pray the additional prayer [on Shabbat, Festivals, and Rosh Chodesh], there is no make-up for it.

7[If] it was on purpose and one did not pray [an Amidah], there is no make-up for it. Even at the prayer that is immediately adjoining it. And if one wanted, one may pray it as a voluntary prayer and one does need an innovation of something new [in it] if one prayed it at the prayer time immediately adjoining it.

8One who did not pray [the Amidah] while there was still enough time to pray because one supposed that time would still remain for one after one finished whatever thing one was involved in, and between one thing and another, the time passed; and similarly, one who was troubled with monetary needs so that one would not incur a loss, and because of that one lost [one's opportunity] to pray; and similarly someone who is drunk and did not pray. All of these are considered people with extenuating circumstances and they [do] have a pan opportunity for] a make-up. Gloss: From the outset, one should not let the prayer time pass because of monetary loss. [T'rumat Hadeshen - Siman 5]

9If one erred and did not pray the afternoon prayer on the eve of Shabbat, one should pray the evening prayer [i.e. Shabbat Amidah] twice; the first is for the evening prayer and the second is the make-up [for the afternoon prayer]. Gloss: similarly, if one did not pray the afternoon prayer on the eve of Rosh Chodesh [the New Month], one prays the Rosh Chodesh [prayer] twice. And if one did not mention "Ya'aleh V'yavo" [i.e. the insertion for Rosh Chodesh] in the first one, but one mentioned it in the second one, one must go back and pray [again]. But if one did not mention it in both of them, or if one mentioned it in the first but not the second, then one does not need to go back ([based on the] Kol Bo, except for what he wrote regarding saying the Rosh Chodesh prayer twice)

10If one erred and did not pray the afternoon prayer on Shabbat, one should pray it upon the [immediately after the end of] Shabbat (two weekday prayers); one separates [Shabbat from weekday i.e. the insertion of "ata chonantanu" into the 4th blessing of the Amidah] in the first, but one does not separate in the second. If one did not separate in the first, but separated in the second, the second prayer counts, but the first prayer does not count. If one separated in both of them, or did not separate in either of them, one has fulfilled one's obligation [for both recitations of the Amidah].

11If one erred during the afternoon prayer of Shabbat and prayed the Eighteen [i.e. the weekday Amidah] and did not mention Shabbat, [immediately after the end of] Shabbat one prays [the Amidah] twice, and does not separate [Shabbat from weekday - i.e. insert "ata chonantanu"] in the second; and it should be prayed according to the law of a voluntary prayer and there is no need to innovate any [new] thing [into it]. The same applies if one did not mention "Ya-aleh V'yavo" during the afternoon prayer of Rosh Chodesh.

12One who erred and mentioned something [belonging to] one of the other days [i.e. a passage or insertion from a different occasion] in one's prayer when it was not its time [to say it], it is not considered an interruption. Gloss: if one realizes that one erred, one stops [saying the incorrect passage], even in the middle of the blessing(Ohr Zarua in Tractate B'rachot)