Is Jesus present in the Eucharist?

Yes, this is what Catholics believe.

At the Last Supper, Jesus said, "Take this bread. It is my body." Then he said, "Take this and drink. This is my blood. Do this in memory of me."

Catholics believe this was the First Eucharist, that through a miracle the bread and wine actually became the body and blood of Jesus Christ.

Catholics reenact the Last Supper during every Mass, where God, acting through the priest, changes the bread and wine into the body and blood of Jesus Christ.

This is a great sacrament of thanksgiving and unity of Catholics.

By the way, the Eastern Catholic, Oriental Orthodox and Eastern Orthodox Churches, the Assyrian Church of the East, the Lutheran and many Anglican Churches also believe in the Real Presence of Jesus Christ in the Eucharist. This is more than half of all Christians in the world.

For more information, see the Catechism of the Catholic Church, sections 1322 and following:

With love in Christ.