Shavuot, which literally means "weeks," is celebrated seven weeks and one day (50 = "pente" in Greek) after the Feast of Firstfruits. Most Christians are familiar with the events of Pentecost in the book of Acts, which was marked by the outpouring of the Holy Spirit. These events are powerful beyond description, and Paul says it is the Spirit of God that brings life.
However, it is a lesser known fact that Shavuot/Pentecost had a powerful previous fulfillment which brings even more meaning to the events recorded in Acts. The day is a wedding day. Just as He did in Acts, God betrothed Himself to Israel (and all who bind themselves to Israel) at Mount Sinai; an act which in the eyes of God is as strong a commitment as marriage. (It is for this reason that Joseph was going to "divorce" Mary, though they had not finalized their marriage.) The events of Acts 2 are a similar wedding ceremony with Israel (and all who bind themselves to the God of Israel) and God consummated this marriage by living inside of us.
The similarities and contrasts in the events that are recorded are noteworthy and again teach us volumes about God's relationship to man. The Lord gave the Torah, His righteous instruction, to His people at Mount Sinai on Shavuot, just as He wrote the Torah on our hearts on Shavuot in the enactment of the new covenant.
In Exodus 19, the events happened at Mt. Sinai, fire rested on the mountain, God wrote His Law on tablets of stone, God came to dwell among His people, about 3000 were slain, there was heard a sound like thunder, and the Israelites purified themselves.
In Acts 2, the events happened at Mt. Zion, fire rested on the disciples, God wrote His Law on our hearts, tablets of flesh, God came to dwell in His people, about 3000 live, there was heard a sound like wind (in Hebrew, wind and spirit are the same word), and believers purified themselves in immersion.
(Similarities and differences such as these can be explored in depth, but suffice it to say here that they are amazingly parallel and worthy of further examination.)
The Jewish tradition about the giving of the Law is equally as significant as the account in Exodus. Tradition says that God's voice was heard in the 70 languages of the nations. In Acts, the exact same terminology is used - the disciples were heard speaking in all the languages of all the nations, spreading the truth of God's redemption and instruction to the world. Jewish tradition also says that all Israel immersed themselves in water before God. It is fulfilling to study and compare the two events to understand God's plan for His people His progressive revelation of Himself and His plan.