Gemara

55b (Mishnah): In Yericho, they were Korech (wrapped together Keri'as) Shema. Chachamim did not protest.

56a (Beraisa - R. Meir): They said the first verse without pausing.

(R. Yehudah): They paused, but they did not say 'Baruch Shem Kevod Malchuso l'Olam va'Ed.'

(Reish Lakish): "Va'Yikra Yakov El Banav va'Yomer He'asfu v'Agidah Lachem" - Yakov wanted to tell his sons Ketz ha'Yamin (the end of days). The Shechinah departed.

Yakov feared that this was because one of his children was improper.

His sons: "Shma Yisrael Hash-m Elokeinu Hash-m Echad" - just like Hash-m is One in your heart, also in ours!

Yakov: Baruch Shem Kevod Malchuso l'Olam va'Ed.

Chachamim thought that perhaps we should not include it in Shma, for Moshe did not write it in the Torah.

On the other hand, we should say it, for Yakov said it!

They enacted to say it quietly.

(R. Yitzchak): This is like a king's daughter who smelled a seasoned cooked food. If she will say [that she wants some], it will be disgraceful for her. If she will not say, she will be in pain.

Her servants brought some for her covertly.

(R. Avahu): They enacted to say [Baruch Shem Kevod... ] aloud, lest heretics claim [that we say heresy at that time].

There are no heretics in Neharda'a, therefore they say it quietly.

Berachos 13a (Mishnah): If one was reading Parshas Shma in the Torah, and it was time for Kri'as Shma, he was Yotzei only if he had intent.

Rishonim

R. Yonah (Berachos 8b DH Hiskinu): They enacted to say Baruch Shem Kevod quietly, and the rest aloud, if he wants. This is the custom is nowadays in many places. It is a good custom, but one must be concerned lest Amei ha'Aretz accustom themselves to speak in between.

Rashba (1:452): In some places people say Shma aloud, and in some places they say it quietly. Chachamim were adamant only about Baruch Shem Kevod, to say it quietly, because Moshe did not say to say it. We say it because Yakov said it.

Poskim

Shulchan Aruch (OC 61:13): After the first verse, one must say Baruch Shem Kevod quietly.

Levush (63:4): If one read the first verse without intent he was not Yotzei. He must read it again. From the first verse and onwards, even if he read without intent, he was Yotzei.

Levush (63:5): Therefore, if one was reading the first verse and was overcome with sleep and cannot intend, people must wake him until he reads it properly awake, with intent. After the first verse, even if he was dozing, he was Yotzei. In this entire matter, the first verse includes Baruch Shem Kevod. It is included in Kabalas Ol Malchus Shamayim. It has all laws of the first verse for this.

Magen Avraham (11): If one did not say Baruch Shem Kevod, he need not return (Bach, Shiltei ha'Giborim). The Levush says that even if one said it without intent, he must go back. Siman 66:1 (see below) connotes like this.

Sha'arei Teshuvah (11): Machazik Berachah brings from Alfasi Zuta that one may not interrupt in the verse of Shema, nor in Baruch Shem Kevod. However, between these two verses is like the middle of a Perek of Keri'as Shema.

Mishnah Berurah (30): Saying it quietly indicates that it is not the Parshah written in the Torah; just Yakov said it.

Bi'ur Halachah (DH Achar): The Magen Avraham connotes that he holds like the Levush, that if one did not say Baruch Shem Kevod, he must return. This means to the beginning, like Chayei Adam (21) proved, or at least to Baruch Shem Kevod. I hold like Shiltei ha'Giborim and the Bach, that he need not return. R. Yehudah says that they did not say Baruch Shem Kevod. Chachamim disapproved, but they did not protest. If he must return, and he was not Yotzei, why didn't they protest, like they protested about other matters that also were not Torah Isurim? Also, why should we make such a big argument between R. Yehudah and R. Meir, who holds that they did not pause? Rashi says that they did not pause between Echad and v'Ahavta. The Maharsha explains that he holds that R. Meir does not require saying Baruch Shem Kevod at all! Surely, R. Yehudah agrees that one who did not say it need not return. Also, in Berachos we say that if one was reading in the Torah (Rashi - Parshas Shema), and had intent, he was Yotzei, even though he did not say Baruch Shem! This shows that one is Yotzei b'Di'eved. If we explain "intent" to mean intent to be Yotzei, we can say that he said also Baruch Shem Kevod. However, if it means intent to read in the Torah, like the Gemara's rejection, surely he did not say it, and even so he was Yotzei! The Yerushalmi says similarly. This supports the Levush.

Note: One could say, unlike Rashi [who says that it discusses one who read Parshas Shma] that the discussion is whether or not he was Yotzei the first verse. If so, there is no proof for the Levush,

Bi'ur Halachah: The Poskim omitted this. Presumably, they explain the Yerushalmi differently. Do not say that the Mishnah is like R. Meir, who does not require saying Baruch Shem Kevod. Firstly, the Yerushalmi says that he requires saying it. Rashi had another text in the Yerushalmi, like the Meforshim say. Also, the Poskim brought the Mishnah Stam, and did not mention that we rule like R. Yehudah. Rather, one is Yotzei in every case. The Magen Avraham brought a proof from 66:1 (one may interrupt in the middle of Baruch Shem Kevod only for mortal danger). This shows that it is part of Kabalas Ol Malchus Shamayim, like the first verse. This is no proof. We agree that saying Baruch Shem Kevod is a great matter. This does not prove that one who omitted it must return to the beginning. If one skipped in the middle of the Parshah, had the Torah not said "v'Hayu" to teach that one may not read out of order, he would not need to return to the beginning! What is the source to be more stringent about Baruch Shem Kevod, which Chachamim added to Keri'as Shema? It seems to me that the Levush agrees. He means only that one must return. It is unlike other verses in Shma, for which one need not return due to [lack of] intent even if he did not yet begin the next verse. However, if he already read Shema, even if he omitted Baruch Shem Kevod, he need not return for this. He merely says it when he remembers. Perhaps even this is not necessary according to letter of the law.

Kaf ha'Chayim (45): The Mechaber (66:1) and many Acharonim connote like the Levush.

Kaf ha'Chayim (47): Even though we say it quietly, he should be slightly audible to his ears.

Shulchan Aruch (63:4): If one said the verse "Shma Yisrael..." without intent, he was not Yotzei, and he must repeat it.

Mishnah Berurah (12): Also Baruch Shem Kevod... must be repeated if it was said without intent.

Shulchan Aruch (66:1): One may interrupt in the middle of Parshiyos of Shma to greet one who he fears, except for the verse of Shma Yisrael and Baruch Shem Kevod. One may not interrupt in them at all, unless he fears lest the person kill him.

Bi'ur Halachah (DH she'Lo): Even though it seems that one does not answer, and so says Chayei Adam, this requires investigation. Above (Bi'ur Halachah), I proved that one who did not say Baruch Shem Kevod need not return to say it, like the Bach and Shiltei ha'Giborim. What is the source to equate it to the verse of Shema to forbid interrupting to answer Amen Yehei Shmei Raba or to Kedushah?

Rema (70:1): Women should read at least the first verse of Shema.

Kaf ha'Chayim (5): They should say also Baruch Shem Kevod.

Shulchan Aruch (619:2): On the night of Yom Kipur and during the day, we say Baruch Shem Kevod loudly.

Source (Gra DH b'Leil): This is from Medrash Rabah at the end of Parshas va'Eschanan.

Kaf ha'Chayim (34, citing the Medrash): When Moshe went up to receive the Torah, he heard the angels praising Hash-m Baruch Shem Kevod... He brought this praise to Yisrael. This is like a man who stole an ornament and gave it to his wife, but told her "wear it only in the house."

Magen Avraham (8): The entire year we say it quietly because Moshe stole it from the angels. On Yom Kipur, also Yisrael resemble angels (Tur). In Siman 61, he wrote that it is because Moshe did not write it in the Torah. I.e. this was to hide it from the angels. Also Hagahos Maimoniyos says so.

Kaf ha'Chayim (35): The Shulchan Aruch connotes that everyone says it aloud. However, Maharikash says that the Shali'ach Tzibur says it aloud, and everyone says it softly with him, like the rest of Shma. Perhaps the Tur and Shulchan Aruch agree.