1. One who is learning Torah:[1]

One who is learning Torah[2] is exempt from wearing Tefillin throughout the day. This means that he is not obligated to stop learning in order to wear them.[3] He is however obligated to wear the Tefillin for Shema and Tefilah.[4] Nevertheless, if the person desires to stop and wear them [by other times of the day], he may wear them even with a blessing.[5]

[1] Admur 38:9; Michaber 38:10 Mechilta Bo 17; Or Zarua 1:531; Mordechai

[2] What topics of Torah learning exempt one from wearing Tefillin? Some Poskim rule that this exemption only applies towards one who is reading the Chumash, and not towards one who is learning Gemara. [M”A 38:13; Tur in name of Baal Haitur; P”M 38 A”A 13] The reason for this is because only in Chumash does it mention Yetzias Mitzrayim. [P”M ibid; Levushei Serud 38:13] However from Admur ibid it is clear that all Torah learning exempts the person as a) He omits this ruling of the M”A ibid and b) He mentions the reason of “Toras Hashem Beficha” and not that of Yetzias Mitzrayim. 

[3] The reason: Although one who is learning Torah is obligated to stop and perform all Mitzvos which cannot be done through others, as explained in Y.D. 240:12 [and Kuntrus Achron 250:2 and 444:18 and Y.D. 246:18 certainly this applies towards Mitzvos which must be done with one’s body] nevertheless he is exempt from wearing Tefillin the entire day as regarding Tefillin it states that “They are a sign on your hand and a reminder between your eyes in order so the Torah of Hashem be on your mouth”, and thus one who already has the word of Hashem on his mouth does not require a sign and reminder. [Admur ibid]

[4] The reason: This is required in order to accept the complete heavenly yoke. [Admur ibid] Vetzaruch Iyun, why here Admur omitted the reason of false testimony.

[5] The reason: Although he is exempt from stopping to wear them, nevertheless, since he desires to stop from his learning, he is therefore obligated to wear the Tefillin as soon as he stops. [Admur ibid] The above implies that a) Today that we anyways do not wear Tefillin throughout the day there is no Nafk Minah between one who is learning and one who is not. B) There is a constant obligation to wear Tefillin throughout the day.