The Ramban calls Sefer Vayikra "Torat Kohanim." The Sefer primarily deals with Korbanot (offerings) and maintaining the sanctity of the Mishkan. Parshat Vayikra deals with Korbanot.
"Speak to the Children of Israel and say to them: When a man among you brings an offering to Hashem: from animals-from the cattle or the flock shall you bring your offering"(1:2). The Rambam records about 100 of the 613 Mitzvot pertaining exclusively to Korbanot. Many others relate to the Temple and the Temple Services.
Korbanot are mistakenly translated "sacrifices" (I may use this translation on occasion as well to drive home a point) when in essence they are "Offerings" to G-d which bring Man closer, more attached and better connected with the Almighty (the root of the word is "Karov" to bring closer). In the Rambam's Moreh Nevuchim (Guide to the Perplexed) 3:32, he claims that Korbanot were originally instituted because Human Nature is such that people cannot instantaneously abandon existing religious practices which the Jews were subjected to in Egypt. The Rambam maintains that the Egyptian idolaters used animal sacrifices in their worship. The Jews were re-directed to use this method of worship towards G-d, Almighty. The Ramban takes issue with the Rambam.
The Ramban argues that animal offerings predated idolatry. This was seen in the cases of both Hevel son of Adam (Genesis 4:4) and Noach (Genesis 8:20). The Ramban maintains that the sinner is using the animal to replace him and should cause him to reflect upon his own mortality and result in repentance. Because of the Rambam's statements in Moreh Nevuchim a minority view holds that there will not be animal offerings at the time of the Third Temple. According to this view our Prayer Services of today will replace animal offerings. I repeat this is only a minority view. The Rav (Rabbi Yosef Dov Soloveitchik Z'TL) in his work "The Halakhic Mind" notes that the Jewish People have in general ignored in a Halakhic sense most of the Rambam's rationalizations in his "Guide to the Perplexed". In point of fact the Rambam himself writing in his Halakhic Opus "Mishneh Torah" mentions Korbanot in the Third Temple. The Rambam states in Hilchot Melachim(11:1) "In the future the Messianic King will arise and renew the Davidic Dynasty, returning it to its initial sovereignty. He will build the Temple and gather the dispersed of Israel. [Then], in his days [the observance of] all the statutes will return to their previous state. We will offer Korbanot, observe the Sabbatical and Jubilee years mentioned in the Torah".
The Rambam is saying unequivocally we will bring Korbanot in the Third Temple. The Rambam does not specify what type of "Korbanot" will be brought. At face value it seems rather clear that the Rambam is talking about all of the Korbanot brought "in their previous state" and "according to all the particulars mentioned in the Torah". This would of course include all of the Animal Offerings. Fast forward to the first Chief Rabbi of Israel, Rabbi Avraham Yitzchak HaCohen Kook, who some claim believed that animal offerings will not be re- instituted when the Third Temple is rebuilt.
It is based on his commentary on the Siddur on the sentence at the end of Shemoneh Esrei, V'arvah LaHashem Minchat Yehuda V'Yerushalayim Kimei Olam Uch'shanim Kadmoniyot"-Then shall the offering of Judah and Jerusalem be pleasant to Hashem as in the days of old and as in the ancient years." (Malachi 3:4) Rav Kook wrote:"In the future, the abundance of knowledge will spread to and penetrate even animals…and the "sacrifices" which will then be from Grain, will be as pleasing to G-d as in days of old (when there were animal offerings)" [Olat Reiyah, Vol.1 (Jerusalem 1983) 292]. This would limit the Third Temple to only Vegetarian Korbanot. However, this does not seem to be the end of the story because Rav Kook writes in Iggrot HaReiyah, Vol.4 [Jerusalem1984]23-5 letter 994 "And regarding "sacrifices", it is more correct to believe that everything will return to its place, and G-d willing, be fulfilled when the Redemption comes, and Prophecy and the Divine Spirit return to Israel".
This suggests strongly that Rav Kook did believe that animal offerings will indeed be part of the Third Temple and that people will have a better understanding and appreciation for animal offerings. His statement on Malachi 3:4 refers to a far-off time past Techiat HaMeitim (Resurrection) when animals will have some level of Human intelligence, in an idyllic world, where only Vegetarian Offerings will be brought. The fact that Conservative Judaism considers "sacrifices" an anathema should make one pause about the whole topic. Conservative Judaism deletes the idea of "sacrifices" in their prayers at every opportunity. The whole section of Korbanot is deleted from their Siddurim. In the Retzei Prayer that was said by the Kohanim at the time of the Temples and we say in Shemoneh Esrei the mention of "offerings" is deleted from their prayer books.
"Be pleased, Hashem our G-d, with thy people Israel and with their prayer; restore the worship to thy most Holy Sanctuary; accept Israel's offerings and prayer with gracious love. May the worship of thy people Israel be ever pleasing to thee". Because of this it is very important to highlight the fact that animal offerings will indeed be re-instituted when the Third Temple is rebuilt. May the Retzei Prayer be granted in its entirety speedily in our day. Shabbat Shalom