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The Kavanos-What should one have in mind when performing the Mitzvah of Tzitzis? 
When placing on the Tallis one is to have in mind that G-d commanded us to wear the Tallis in order to remember all of His commands and consequently fulfill them. [This is aside for the general intent that one must have prior to fulfilling any Mitzvah; that one must intend to perform it in order to fulfill the command of Hashem. One who wears Tzitzis without even this intent does not fulfill the Mitzvah at all. One who wears the Tzitzis in order to fulfill the Mitzvah of Tzitzis, but without intending to do so in order to remember all of the Mitzvos, has not fulfilled the Mitzvah in its proper fashion. He is not fulfilling the true intent behind this Mitzvah, and is considered to fulfill the Mitzvah out of mere habit rather than of true religious fervor. When wearing the Tzitzis one is to also have in mind to draw upon himself the Kingship of Heaven. If one did not have the above intent in mind at the time of the blessing then he is to do so anytime while still wearing the Tallis.]
Practically, if one did not have explicit intent to wear the Tzitzis in order to fulfill the Mitzvah does he fulfill his obligation? If one put on Tzitzis casually without having anything in mind, does he fulfill the Mitzvah?
Some Poskim rule that we only say that one does not fulfill the Mitzvah without explicit intent if it is possible that he intended on doing the action of the Mitzvah for other purposes. [Thus, when wearing a Tallis simply in order to warm himself up from the cold, or to go up for Duchan, then explicit intent is required in order to fulfill the Mitzvah.] If however it is clearly evident that he did the action for the sake of the Mitzvah [such as a typical person who puts on his Tallis Gadol/Katan in the morning], then he fulfills his obligation even if he did not have explicit intent. Nevertheless initially one is to have explicit intent before the Mitzvah.
If one put on Tzitzis not for the sake of the Mitzvah, such as simply because he is cold, is it considered as if he is wearing a four cornered garment without Tzitzis?
Some Poskim rule that when lack of intention disqualifies the Mitzvah of Tzitzis, it is considered as if one is wearing a four cornered garment without Tzitzis and he is thus transgressing a positive command by wearing it. The Poskim however negate this opinion, as although he does not fulfill the Mitzvah, nonetheless it is not considered that he is wearing a four cornered garment without Tzitzis.
Must one have the above intents upon wearing a Tallis even if he is wearing it without a blessing, such as those who are married and wear a Tallis Katan without a blessing?
Yes. The above Kavana relates to the Mitzvah and not to the blessing, and hence it is relevant whenever one wears a Tallis Gadol/Katan, even if a blessing is not recited.
The ruling of Bach-Importance of intent specifically by the Mitzvah of Tzitzis:
The Bach rules that since the verse states that the purpose of the Mitzvah of Tzitzis is to remember the Mitzvos, therefore the main fulfillment of this Mitzvah is dependent on having the above Kavana upon fulfilling the Mitzvah. This is in contrast to the other Mitzvos, in which case one fulfills his obligation so long as he intended to fulfill the command of Hashem, even if he did not have in mind the particular intent of the command. Thus, one who fulfills the Mitzvah of Tzitzis without having the above matter in his mind, has not fulfilled the Mitzvah in its proper fashion.
An auspicious time to be saved from bad character traits:
When one puts on his Tzitzis it is an auspicious time to Daven to Hashem to be saved from bad emotions and character traits such as anger, jealousy and hatred.
The Kabalistic intents:
The Arizal writes that when putting on the Tallis one is to intend that the 32 strings correspond to the 32 paths of wisdom. Doing so is a Segula for avoiding pain in one’s teeth, of which there are also 32 in number.
 8/17; Siddur Admur; Tanya 41; Michaber 8/8; Levush 8/9
 As the verse states “And you will see them and remember all the commands of Hashem.” [ibid]
 See Admur 60/5
 If one does not have this intent then he does not fulfill his obligation as explained in 60/5. [There Admur brings a dispute regarding whether Mitzvos require intent and he rules like the stringent opinion.] See Biur Halacha 60/4 “Veyeish Omrim”; Vetzaruch Iyun, as the entire Mitzvah of Tzitzis is when one desires to wear a four cornered garment for the sake of clothing his body, and hence one’s main intent is to cover his body, and not for the Mitzvah. One must say that although one’s main intent in wearing the garment is for benefiting his body, he must intend that the reasons why it contains Tzitzis is for the sake of fulfilling the Mitzvah of Hashem.
 Bach 625; Elya Raba 8/9; Chesed Lealafim; Kaf Hachaim 8/32
 Biur Hagr”a 8; Ben Ish Chaiy Bereishis 1; Chesed Lealafim; Kaf Hachaim 8/32
 Tanya ibid in name of Zohar 3/120; Vetzaruch Iyun from 25/5; 66/3 and 11 that only Tefillin has “Kabalas Ol Malchus Shamayim” and not Tzitzis.
 Piskeiy Teshuvos 8/18
 M”B 60/10; Biur Halacha 60 “Vechein Halacha”
 Chayeh Adam Klal 68
 See Shaareiy Ephraim brought in Biur Halacha 14/3 “Ubesefer” and 60/4 “Veyeish Omrim”
 Thus, if he read Shema during prayer or ate Matzah during the Seder or blew Shofar or shook Lulav he fulfills his obligation even if he did not have explicit intent, as it is clearly evident that he is only doing these matters in order to do the Mitzvah. [ibid]
 Biur Halacha 60/4 “Veyeish Omrim”
 Minchas Shlomo 1/1; Yeshuos Moshe 3/58; Even Yisrael 8/1; 9/8; Piskeiy Teshuvos 8/19; See Minchas Chinuch 325
 Bach 8 and 625; See Likkutei Sichos 33/101
 Bach 8
 Bach 625
 Kav Hayashar 85
 Kaf Hachaim 24/11
 Shaar Hakavanos Tzitzis 7
 Chesed Lealafim 24/3; See also Shulchan Menachem 5/253 that checking the Tzitzis is a Segula to remove tooth pain.