Gemara

39a (Mishnah): The Mitzvah is for the oldest brother to do Yibum. If he does not want, we see if the other brothers want. If they don't, we tell the oldest 'it is your Mitzvah; do Chalitzah or Yibum.'

Even if he wants to wait for a brother who is a minor to grow up, or for the oldest brother to return from overseas, we tell him to do Chalitzah or Yibum now.

R. Yochanan and R. Yehoshua Ben Levi argued about whether Yibum of a younger brother is better, or Chalitzah of the oldest.

Question (Mishnah): If the oldest said to wait for a brother to grow up, we do not hearken.

According to the opinion that prefers Yibum of a younger brother, we should wait, perhaps he will do Yibum!

Counter-question: According to everyone, why don't we wait for the oldest brother to return from overseas? Perhaps he will do Yibum!

Answer to both questions: You must say that we do not delay the Mitzvah.

47b (Beraisa): If he still wants to convert (after hearing about some Mitzvos), we circumcise him immediately.

This is because we do not delay a Mitzvah.

Yoma 33a (Reish Lakish): We do not pass over Mitzvos.

Megilah 6b (Beraisa - R. Shimon ben Gamliel): If the Megilah was read in the first Adar, and the year was declared to be a leap year, we read it again in the second Adar.

R. Eliezer b'Rebbi R. Yosi says, we do not read it in the second.

(R. Chiya bar Avin): The Halachah follows R. Shimon ben Gamliel.

(R. Yochanan): R. Eliezer and R. Shimon both learned from the same verse, "In every year":

R. Eliezer says that every year, we celebrate in the month next to Shevat;

R. Shimon says that every year we celebrate in the month adjacent to Nisan.

R. Eliezer's reason is because we do not pass over Mitzvos.

Mechilta (Shemos 12:17): R. Yoshiyah says, we read "U'Shmartem Es ha'Matzos" as if it said 'ha'Mitzvos' to teach that just like we do allow (dough for) Matzos to become Chametz, we do not sour Mitzvos (by delaying them). Rather, one does a Mitzvah at the first opportunity.

Menachos 64b (Mishnah): L'Chatchilah, the Omer must be brought from a place close (to Yerushalayim);

If no barley near Yerushalayim is ripe, it may be brought from anywhere (in Eretz Yisrael).

(Gemara) Question: Why must it be brought from a close place?

Answer #1 The Omer must be Karmel (soft. If it was brought from afar, it could dry up.)

Answer #2: We do not pass over Mitzvos (once we find a suitable place, we do the Mitzvah immediately.)

Rishonim

Rashi (Yoma 33a DH Ein): The Mechilta teaches that Ein Ma'avirin Al ha'Mitzvah, for then it is delayed and sours.

Tosfos (Menachos 64b DH Iba'is) and Piskei Tosfos (Yoma 58b 36): Ein Ma'avirin Al Mitzvos applies only when both are in front of us and we do not know which to do first.

Rebuttal #1 (Shitah Mekubetzes Menachos 64b 11): The Gemara says that Ein Ma'avirin Al Mitzvos applies to the Omer, even though there is only one Mitzvah to do.

Rebuttal #2 (Tosfos Megilah 6b DH Mistaber): R. Eliezer b'Rebbi Yosi says that we read the Megilah in Adar Rishon because Ein Ma'avirin Al Mitzvos, even though there is only one Mitzvah to do.

Defense (Yad Binyamin Menachos 64b DH v'Lashon and DH v'Achen): Tosfos teaches that if the Torah fixed a place for a Mitzvah, e.g. on which side of the Mizbe'ach blood must be put, Ein Ma'avirin cannot determine the place. Tosfos agrees that Ein Ma'avirin applies to one Mitzvah when the Torah did not fix a place. The Malbim explains that Tosfos says that Ein Ma'avirin overrides Tadir (the more frequent Mitzvah) only when there are two Mitzvos to do. When there is only one Mitzvah, we pass over a Mitzvah to do what is more Tadir.

Yad Binyamin (ibid. DH v'Iba'is): Tosfos asked why the Torah needed to write "Karmel". This shows that he holds that Ein Ma'avirin is mid'Oraisa. This is unlike the Radvaz (1:529), who says that it is mid'Rabanan, and the Drashah in the Mechilta is an Asmachta.

Note: Perhaps Piskei Tosfos holds that the reasons given regarding the Omer argue with each other. He rules that Ein Ma'avirin does not apply since one will reap only one of them. He would agree that Ein Ma'avirin applies if one needs to reap in two places, but this would not answer the Gemara's question about why the Omer is brought from nearby.

Poskim

Shulchan Aruch (OC 109:1): If one enters a Beis ha'Keneses and finds the Tzibur praying Shemoneh Esre, he should not begin unless he can finish in time to answer to Kedushah.

Bi'ur Halachah (DH ha'Nichnas): If one prays at length and does not finish in time for Kedushah even if he starts at the same time as the Tzibur, perhaps he may begin, for this is proper Tefilah b'Tzibur. Also, now he is obligated to pray; the obligation to answer to Kedushah is not yet upon him. We must investigate why the Shulchan Aruch is not concerned for passing over Mitzvos.

Shulchan Aruch (274:1): (On Shabbos) one makes ha'Motzi on two full loaves and cuts the bottom one.

Rema: This is only on Shabbos night. On Shabbos day or Yom Tov night we cut the top one. The reason is based on Kabalah.

Rebuttal (Bach): One cannot transgress the Gemara, which says that Ein Ma'avirin Al Mitzvos, to fulfill the Kabalah! We wear Tefilin on Chol ha'Mo'ed like the Yerushalmi says, even though the Zohar says that one is Chayav Misah for this!

Mishnah Berurah (5): The Taz (when cutting the bottom loaf) would position the bottom loaf closer to himself, to avoid passing over a Mitzvah. Alternatively, one may take the top loaf at the time of the Berachah and bring it under the other loaf and cut it.

Kaf ha'Chayim (2): According to the Ari Zal, whose Kabalah is from Eliyahu ha'Navi, one cuts the top loaf by day and by night.

Shulchan Aruch (426:2): We bless Kidush Levanah only on Motza'ei Shabbos.

Rema: We wait for Motza'ei Shabbos only if it will be before the 10th of the month. We do not wait longer lest there will be cloudy nights and the time for the Mitzvah will pass.

Shulchan Aruch (568:7): If a parent died in Adar, in a leap year one fasts on the corresponding day in the second Adar.

Rema: Some say that he fasts in the first Adar.

Mishnah Berurah (568 41): The Mechaber holds that Stam Adar is Adar Sheni. Some say the opposite. Also, we do not pass over Mitzvos.

Gra (7): One should fast in both months. R. Shimon ben Gamliel argues about the Parashiyos, but he agrees to the first Tana that everything else applies in both months. Megilas Ta'anis also says so.

Sha'arei Teshuvah (651 17): The Magen Avraham (25:2) says that if at the time of Hallel one was given a Kosher Esrog, and he knows that an hour or two later he will have a Mehudar Esrog, it is not proper to delay the Mitzvah. He learns from Yevamos 39a. Beis Yakov (Teshuvah 142) explains 'if he agrees to be circumcised we do so immediately' that any time during that day is called immediately. Tzemach Tzedek says similarly regarding one who swore to pay immediately; after the day is called delaying the Mitzvah. However, if one is sure that later he will be able to do the Mitzvah ideally, he may delay even a long time. This is also Zariz. His intent to do the Mitzvah ideally is considered the start of the Mitzvah. (Regarding Milah the custom is to circumcise in the morning.) According to this, one should wait for a nicer Esrog.