What is one to do if he is in middle of Shemoneh Esrei, and the congregation began to read Kerias Hatorah?
It is debated amongst the Rishonim and Poskim as to whether one is to stop and listen to a Davar Shebekdedusha in the midst of Shemoneh Esrei, or not, and practically we rule that one is to stop and listen silently. However, some Poskim write that this ruling does not apply to Kerias Hatorah, and it is thus better to continue with the Davening then to stop and listen to the Keria in middle of Shemoneh Esrei. This applies even if one will not be able to hear Kerias Hatorah again that day. However, other Poskim rule that one may [and should] stop and listen to the Keria. [Practically, it is best to avoid this situation and not begin Shemoneh Esrei at a time that will conflict with Kerias Hatorah. However, Bedieved if one did so, or must do so due to the passing of Zman Tefila, then those who stop and listen have upon whom to rely. This especially applies if one cannot properly concentrate on his Shemoneh Esrei in the midst of Kerias Hatorah.]
Women: According to most Poskim, and the final ruling, women are not obligated to hear Kerias Hatorah and hence they may continue Shemoneh Esrei rather than to stop and listen to Keiras Hatorah. Nonetheless, if a woman cannot properly concentrate on her Shemoneh Esrei in the midst of Kerias Hatorah then she may stop and listen, as stated above.
 Admur 104:5; Michaber 104:7; Tur 104:7 in name of Rabbeinu Chananel; Tosafus Brachos ibid that so is the custom; Rashi Sukkah 38b; Bahag Brachos ibid; Haeshkol p. 31 in name Rav Haiy Gaon; Ran 19b; Ravayah; Bach 104 in name of Mordechai and that so is custom; Levush 104; Soles Belula 104:2; Chayeh Adam 25:10; Beis Oved 57; Kitzur SHU”A 18:14; Ben Ish Chaiy Mishpatim 5; Kaf Hachaim 104:36
Other opinions: Some Poskim rule one is to continue Davening, as hearing is like answering, and is considered a Hefsek. [2nd opinion in Tur ibid in name of Rabbeinu Tam and Ri; Tosafus Brachos ibid in name of Rabbeinu Tam and Ri and Geonim; Hagahos Maimanis Tefila 10; The Rosh Brachos 18 and Rabbeinu Yona 13b bring both opinions and give no arbitration; See Beis Yosef 104:7] Other Poskim rule that although it is not considered a Hefsek, one is not Yotzei being that he is not allowed to speak, and hence there is no point of stopping to listen. [Darkei Moshe 104:1 in name of the Iggur that the custom of the Ashkenazi Rabbeim is not to stop and listen; Beis Yosef 25 in name of Rashba and Iggur; Shagas Aryeh 6 in name of Shivlei Haleket; Abudarham, brought in Erech Hashulchan 104:3 and 55:1; See P”M 104 A”A 7] Due to the above opinions. Kaf Hachaim ibid concludes that if stopping to listen will ruin one’s concentration of the prayer, or if he anyways cannot hear the Chazan properly, then one may continue his Davening and rely on the other opinions.
 Koveitz Mibeis Levi 12; Teshuvos Vehanhagos 2:70; Piskeiy Teshuvos 104:15 and 135 footnote 13; See Orchos Rabbeinu 3:215 in name of Chazon Ish that if one went ahead and did so he is nevertheless Yotzei; See also Michaber 146:2 for the five opinions regarding learning Torah during the reading.
 The reason: As the above matter of stopping for a Davar Shebekedusha is debated amongst the Poskim and we are only lenient due to the custom. Now, regarding Kerias Hatorah, it was not mentioned in the above Poskim who say to stop and listen, and there was never a Minhag to stop and listen. Therefore, it is better to abstain and not stop to listen to suspect for the Poskim who rule it is an interval. [Piskeiy Teshuvos 104:15] Furthermore, most Poskim rule there is no obligation for every individual to hear Kerias Hatorah, and it is rather an obligation on the congregation. [See Poskim in Piskeiy Teshuvos 135:2 footnote 12]
 Piskeiy Teshuvos ibid
 Az Nidbaru 14:29
 The reason: As we rule that one should stop and listen for a Davar Shebekedusha, and if we rule this way regarding a matter that requires answering, certainly we should rule this way regarding a matter that does not require answering. [Az Nidbaru ibid] Furthermore, some Poskim rule it is an obligation upon every individual to hear every word of Kerias Hatorah [See Poskim in Piskeiy Teshuvos 135:2 footnote 12], in contrast to Kaddish and Kedusha which is not an actual obligation for everyone to hear, and only if one is with a Minyan is he required to answer.
 See Admur 98:1 “If he gets a foreign thought during Davening [Shemoneh Esrei] he is to be quiet until the thought leaves him.”; Shaareiy Teshuva 104; Ketzos Hashulchan 20:20 regarding a child crying
 Maharsham 1:158 that so is explicitly ruled in Ran Megillah 4; Hisorerus Teshuvah 1:5; Beir Moshe 8:86; Piskeiy Teshuvos 135:2
Other opinions: Some Poskim rule women are obligated in Kerias Hatorah. [M”A 282:6, brought in M”B 282:12]
 M”B 282:12 that so is the custom