Yes, Islam recognizes, respects and believes in Jesus (Peace be upon him).
Believing in Jesus (Peace be upon him) is a part of the fundamental Islamic faith, but Islam does not see Jesus as the son of God.
Islam considers God to be beyond humanly relations.

Islam recognizes Jesus as one of the great Messengers of God like Noah, Abraham, Ishmael, Isaac, Lot, Moses, Solomon, David, John, Job, Ezekiel, Jacob and many others (Peace be upon them). Muslims believe in all Messengers of God and also believe that Adam was the first Messenger of God and Muhammad was the final one (Peace be upon them). God sent Jesus about 600 years before Muhammad (Peace be upon them) for the guidance of mankind.

Since the Bible was compiled almost 200 years after Jesus (Peace be upon him), Muslims believe that the actual Message of God brought by him was altered, modified and lost (many versions of the Bible which are currently available differ from each other), therefore God sent His Message for the last time through Muhammad (Peace be upon him). The original text of the Bible is not in use anywhere.

While believing in Jesus as a great Messenger of God, it firmly rejects the irrational doctrine of trinity. Islam clearly differentiates between the Creator and His creations.

Islam also believes in the miraculous birth of Jesus (Peace be upon him) to his mother Mary without any male intervention. A complete chapter of the Qur-an is named after Mary (Chapter 19).

Islam also believes in the God-given miracles performed by Jesus.

Islam believes that God saved Jesus from his Jewish tormentors before they could crucify him.
Islam also believes that God Almighty did not have to get Jesus killed to save humanity.

Muslims use utmost respect while saying, writing or reading the name of Jesus and the other Messengers of God. They always use peace be upon him as a suffix to the name.