Who wrote the first four books of the New Testament?

Matthew a disciple of Jesus wrote the first four chapters. But maybe you mean books?

The first four books are called the gospels and were written by Matthew, Mark, Luke and John.

Matthew the tax collector, also called Levi, wrote the First Gospel.

John Mark is generally accepted as the author of the second gospel. He was the son of Mary of Jerusalem, who owned a house there which the Christians used as a meeting place.

Luke, a physician by profession and a long time companion of Paul, is the writer of the third gospel.

The last gospel, the gospel according to John, is anonymous as to authorship, but there are many good reasons for believing that it was written by the Apostle John, one of the twelve.