The following is an ongoing project which will be updated each year
Commanding the Kohanim:
Hashem spoke to Moshe and told him to command Ahron and his children the following laws [of Karbanos].
Why does the Torah in this instance use the term “Tzav/command” instead of its usual term of “Daber/speak”?
As the word Tzav implies alacrity, as Hashem wanted to give extra motivation and eagerness to the Kohanim for them to fulfill the commands of the Karbanos eternally. As for why specifically the Mitzvah of Karbanos require this special form of command, various explanations have been given:
2. Since the night time is a time of sleep, and the Kohanim are commanded to verify that the limbs of the Karbanos remain on the fire throughout the night, they therefore require extra motivation to prevent them from sleep.
3. This verse is juxtaposed to the last verse of the previous Parsha which concludes with the words “Uliashma Ba.” It is coming to teach us that one is expected to have alacrity in his Torah learning as a mistake due to ignorance is considered as if it was done advertently.
4. Alternatively, the term Tzav implies [not alacrity but] eternity, and is teaching us that the Mitzvah of Karbanos began as soon as they were commanded and will be everlasting.
The laws of the Olah:
This is the law of the Olah offering which is brought onto the altar throughout the night until morning. [This verse teaches us that that the limbs and fats of the animal are valid to be offered onto the altar throughout the night. It also teaches us that even invalid Karbanos, once they are brought to the altar, do not have to be taken down. Nonetheless, there are a few exceptions to this rule, such as an animal that was invalid even before it made it to the altar, and invalid Nesachim [wine libations], or the Nesachim of an invalid Karban, in which case if they are to be taken down from the altar.]
The fire of the altar is to remain on it. [This is coming to teach us that the fire of the altar is to remain eternally lit. Alternatively, it is teaching us that the fire of the altar is not to trespass the boundaries of the altar. Alternatively, it is teaching us that the fire of the inner Mizbeiach is to be ignited using the fire of the outer Mizbeiach.]
Why are the laws of the Olah repeated in our Parsha if they were already mentioned in Parshas Vayikra?
All the Karbanos mentioned in Parshas Vayikra are repeated in later Parshiyos in order to teach all the relevant laws applicable to them which were not brought in Parshas Vayikra.
Which was the greatest of all the Karbanos?
The Olah. This can be seen from the fact that it was the only Karban which was completely consumed by Hashem. It also had the greatest effect of atonement.
For which sins did the Olah Karban bring atonement?
It brought atonement for the nullification of positive commands and the sin of evil thoughts
How was the fire on the altar kept eternally lit?
The Kohanim were commanded to place every day many pieces of wood on the altar in order to prevent the fire from ever extinguishing. If the Kohanim were lazy and irresponsible, causing the fire to extinguish they would transgress a negative command.
Terumas Hadeshen-Cleaning the ash:
The Kohen is to wear an exact measurement shirt of linen, and pants of linen he is to wear on his skin. He is to then remove the ash of the sacrifices from the altar and place the ash near the altar. He is then to remove his clothing and wear other clothing and remove the ash outside of the encampment, however within a holy area. [There were two removals of ash from the altar, one which was done daily and only removed a small portion of the ash, and one which was done on occasion, when the altar became filled with too much ash, in which case all the ash was removed. During the daily removal of a shovel’s worth the regular Kehuna clothing were worn, however when removing the rest of the ash on occasion, a change of clothing was required. See Q&A!]
Was the Kohen allowed to wear any underclothing in-between his skin and his pants?
No. It was forbidden for the Kohen to wear any garment which intervened between his skin and the pants.
Was the Kohen required to wear the other Bigdei Kehuna upon removing the ash, such as the turban and belt?
Yes. The Kohen had to wear all four garments of Kehuna. The reason the verse only states the shirt and pants is to teach us that they must be made into the correct size for each Kohen and that the Kohen may not have an interval between the garment and his skin.
How much ash was required to be removed from the altar?
The Kohen did not take all of the ash off of the Mizbeiach but rather a mere shovels worth. It was therefore called a Teruma, similar to the Teruma/tithe separation taken from food.
How often was the ash of the Mizbeiach removed?
A shovels worth of ash [i.e. Terumas Hadeshen] from the Mizbeiach was removed every morning, prior to the morning Tamid offering. This was a daily obligation. The remaining ash was only removed when necessary, and was not a daily obligation.
Why did the Kohen change clothing prior to the occasional cleaning of ash from the altar?
As it is not befitting for the Kohen to serve Hashem later on with the same clothing which he dirtied in the process of cleaning the ash of the altar.
Was the Kohen obligated to change clothing prior to the occasional removal of ash from the altar?
Some learn that this matter was voluntary, although was encouraged due to the reasons of Derech Eretz explained above. However others learn that it was an absolute obligation for the Kohen to change clothing, as itw as obligatory for him to serve Hashem with clean clothing.
What clothing did the Kohen change into when performing the occasional cleaning of ash from the altar?
Some learn that the Kohen had to change into other lesser quality clothing of Kehuna, as also the occasional removal of the ash had to be performed with the Bigdei Kehuna. Others however learn that there was no need to wear the Bigdei Kehuna during the occasional removal of ash, and it could be removed even while wearing mundane clothing.
Removal of ash represents cleanliness of soul after sin:
After a sinner has received retribution for his sin one must make the sin forgotten. One is not to mention to him of his previous ways. This hints to the experience of the soul in the next world that after it passes the refining river of Dinor, which is a stage of purgatory, the soul is to be respected as it is a princess, the daughter of the king and a Baal Teshuvah. This is the meaning of removing the ash from the altar, remove any remembrance of sin from the person who brought the offering.
Changing clothing-Reincarnation of souls into different bodies:
The changing of the clothing discussed in this verse hints to the changing of clothing of the soul, as every soul passes through many Gilgulim, reincarnations. The verse thus tells the soul, remove your current clothing of the body and wear a differing body as clothing.
 Rashi ibid in his explanation of Toras Kohanim 1/1
 As the Jewish people give up an animal for the sake of the Karban. [Ramban ibid] Now, although this loss of money is for the regular Jew and not the Kohanim, and on the contrary, the Kohen actually benefits from the sacrifice, nevertheless there are sacrifices of the Kohanim which they do not benefit from, such as the Minchas Chvitium. [Ramban ibid in second explanation] Alternatively, since when a Karban is invalid another Karban must be brought in its place, therefore it is considered a command that contains monetary loss. [Chizkuni ibid; See Keli Yakra ibid and Or Hachaim ibid for other explanations]
 Toras Kohanim 1/1; Rashi ibid
 Keli Yakra ibid
 Baal Haturm ibid
 Toras Kohanim ibid as explained Ramban ibid
 Mgeillah 21a; Rashi ibid
 Toras Kohanim 1/7; Rashi ibid
 Rashi ibid that it excludes Haroveia Vehanirba [animals that were involved in bestiality].
 Ramban ibid
 Ramban ibid
 Even Ezra ibid
 Toras Kohanim 1/16; Chizkuni ibid
 Rashbam ibid
 Rabbeinu Bechayeh ibid
 Admur Basar 1/9
 Ramban ibid
 Zevachim 19a; Rashi ibid
 Ramban ibid
 Yuma 20a; Rashi ibid
 Rashi ibid; Rashbam ibid
 Yuma 23b; Rashi ibid
 Rashi ibid
 Ramban ibid
 Dispute in Yuma ibid; Ramban ibid
 Shelah Hakadosh Derech Chaim Tzav
 Shelah Hakadosh Ner Mitzvah Tzav