"When he called to Moshe, HaShem spoke to him from the Tent of Meeting saying: 'Speak to the children of Israel and say to them: "When any person among you offers a sacrifice to HaShem from the animals, from the cattle or from the flock you shall offer sacrifices." ' " (Leviticus 1:1-2)
From the beginning of parshat Teruma (Exodus 25), the rest of the book of Exodus (apart from the hiatus of the episode of the golden calf) describes the preparations for, and building of, the Mishkan. Hence, 447 out of Exodus's 1,209 verses are dedicated to the Mishkan. By the end of the Book of Exodus, the Mishkan has been constructed, all its accouterments are in place, and Moshe is ready to bring the first sacrifices. And the logical progression is the book of Leviticus, commanding the sacrifices.
The book of Exodus spans 140 years - from Jacob and his sons' descent to Egypt until the second year after the Exodus (Exodus 40:17). The primary theme of Exodus is the creation of Israel as a nation and its redemption from Egypt, paralleling the Creation in Genesis; for this reason, Exodus is also called the Book of Redemption (see the Ramban's introduction and poetic epilogue to Exodus).
The entire narrative of Leviticus spans one month - from the first of Nissan in the second year of the Exodus (Exodus 40:17) to the first of Iyar in the same year (1:1). Its entire theme is sacrifice. To be sure, other topics are mentioned, but as the Ramban makes clear, these other topics are directly related to sacrifice. The list of forbidden animals (chapter 11), for instance, is inextricably intertwined with animal sacrifice (see the Ramban on Leviticus 1:1 and 11:1). Similarly, the list of forbidden relationships enumerated in chapter 18 is a direct continuation of the laws concerning the sacrifice brought by a man who experiences seminal discharge (15:13-15) and by a woman who becomes ritually impure (verses 19-30).

The chronological context of Vayikra teaches a crucial lesson regarding sacrifices.

In the same vein, the festivals (chapter 23) and their celebrations center around the Temple sacrifices: "Israel was commanded to fulfill three positive mitzvot on each of the three festivals: to appear before HaShem... and to bring the festival sacrifices... and to rejoice." (Rambam, Hilchot Hagigah- "Laws of Festive Offerings" 1:1). This is the reason that, in classical literature, the book of Leviticus is called Torat Kohanim - it deals primarily with all the issues for which the Kohanim are responsible.
The chronological context of Vayikra teaches a crucial lesson regarding sacrifices. This narrative begins just over eight months after the sin of the Golden Calf, and three months before Moshe would send the 12 spies to spy out the land of Canaan with the intention of conquering it (Numbers 13) - that is to say, between two heinous sins that the nation as a whole committed, at the time when our national spiritual level was presumably somewhat low. Indeed, Rabbi Akiva went so far as to state, "The generation of the desert have no portion in the world to come, neither will they stand in judgment." (Sanhedrin 10:3)
It was precisely that generation, at that juncture, that was commanded to build the Mishkan and to bring sacrifices. This is the clear disproof of the all-too-common argument today that, at present, "we are not on a high enough spiritual level to rebuild the holy Temple and to offer sacrifices." The truth is precisely the opposite: it is exactly when we are on a low level that the Holy Temple, and the sacrifices therein, are even more urgent and important. Or, in the words of the Pesach Haggadah, "He built us the holy Temple to atone for all our sins."
In the above-quoted Mishna, Rabbi Eliezer disagrees with Rabbi Akiva: "Rabbi Eliezer says: 'The generation of the desert do enter the world-to-come, as it says (Psalms 50:5), "Gather unto Me My pious ones, who seal My covenant over sacrifices." ' " (Sanhedrin 110b) Rashi (ad loc) clarifies: "That is to say, the generation of the desert sealed the covenant with God over sacrifices and peace offerings, as it says, 'And they slaughtered bulls to HaShem as peace offerings' (Exodus 24:5), and also, 'Moshe took the blood and threw it over the nation, saying: "Behold the blood of the covenant that HaShem has sealed with you. (Exodus 24:8)" ' "
The moral is clear. It was precisely the sacrifices that the generation of the desert offered that saved them. And in our generation, perhaps the greatest tragedy is that so many of us do not even feel lack of sacrifices.
In the beautifully poetic summarization of the Rambam (Hilchot Me'ilah- "Laws of Misappropriation" 8:8): "All of the sacrifices, without exception, are included in the category of hukkim [laws for which we cannot understand the reason]. And the sages therefore stated: 'On the sacrificial service the world stands.' (Pirkei Avot 1:2) Because by fulfilling these laws, the upright merit life in the world-to-come. The Torah commanded the hukkim before [laws whose reasons we can understand], as it says: 'And you will observe my hukkim and my mishpatim, which a man will do and live by them. (Leviticus 18:5)' "