It is customary amongst many people to celebrate their birthday. It is a happy day in which people yearn and desire to be cherished and allow themselves extravagances and luxuries that they would usually not partake in. In the secular world, many use the day for partying and sometimes partaking in lustful or sinful behaviors. The question with regards to a Jew is whether such behavior is encouraged or discouraged by the Torah. The Rebbe, seeing a birthday celebration as a great opportunity to bring change to the person and his service of G-d, dedicated a great deal of talks and writing to the subject of birthday celebration, and encouraged every person to celebrate their birthday in a way that will bring them closer to Hashem.
Source in the Torah for celebrating a birthday:
The Torah makes mention of a birthday celebration in reference to Pharaoh when he celebrated his birthday and requested his imprisoned head baker and vintner to appear before him, as predicted in Pharaoh’s dream. The Midrash comments on this that majority of people are accustomed to celebrate their day of birth and make a party or celebratory meal in its honor. This is further stated in the Poskim that a birthday is cordially celebrated by some through making a festive meal, and so was the custom of the Ben Ish Chaiy.
The auspiciousness of a birthday:
On one’s birthday, one’s Mazal is dominant and assists him. This is learned from the Talmud Yerushalmi which states that the Amalekites positioned those soldiers who had birthdays that day to enter battle with Bnei Yisrael. The reason for this is because on that day one’s Mazal shines and gives him assistance in battle. What then did Moshe do? He mixed up the constellations, hence removing the Divine assistance from the Amalek birthday soldiers. The same then applies for every person, that his Mazal shines on this day. The same downward flow of Divine light is elicited afresh on the same day every year; it follows that a person should be spiritually aroused on his birthday every year.
Utilizing the day:
Every man, woman and child is to utilize his/her birthday to strengthen and add in all matters of his Judaism, in Torah and Mitzvos, and in the three pillars of Torah, Tefilla and Tzedaka. One is to take upon himself new resolutions for the coming year.
The birthday of a child:
The parents are to celebrate the birthday of their children. This applies to children of all ages, beginning with a child’s first birthday. The parent is to utilize the day to give thanks to Hashem for the gift of having the child and make appropriate resolutions for the proper education of the child. When the child is too young to perform the birthday customs himself, they are to be performed by the parents, such as increasing in learning Torah and giving charity.
 Sechel Tov Vayeishev 20
 Ginzei Yosef 4; Ben Ish Chaiy Rei 17
 Note of the Rebbe Shlita in Sefer HaMaamarim 5702, p. 143
 Yerushlami Rosh Hoshana 3/8
 Hisvadyus 1988 vol. 3 p. 152 
 Hisvadyus 1982 4/2190
 Hisvadyus 1988 vol. 3 p. 153 footnote 25