Each gospel has its own introduction.
In addition to the introduction given directly from the Bible, it can also be informative and helpful to read the introduction to each book that study bibles usually provide. The insights these introductions provide can help us relate to both the author and the intended audience of the book. Keep in mind that the study bible intros are merely scholarly opinions, though, and not to be treated as authoritative with the text itself.
The authors of the Synoptic Gospels (Matthew, Mark, and Luke) are historically assumed by tradition, and more recently by scholarly research - although there is some contention as to whether Matthew is really the author given his apparent reliance on Mark when he was a direct disciple of Jesus.
There’s is no debate about John being the author of his gospel.
There are various websites that offer introductions and overviews of each book of the Bible. One good place to start is at blueletterbible.org.
Matthew
ESV Global Study Bible - Intro to Matthew
Matthew’s gospel is geared more toward a Jewish audience. From his terminology to his lack of explanation of typical Jewish customs, to the structure of his text as a new Tanak, Matthew’s audience was written from a predominantly Jewish perspective. Not that he wanted to exclude others, but that his text would be well understood by Jews.
Mark
ESV Global Study Bible - Intro to Mark
Mark’s gospel was written for a gentile audience, and perhaps even specifically a Roman audience.
Luke
ESV Global Study Bible - Intro to Luke
Luke’s gospel was probably written for a patron - a wealthy individual who paid him for his work on it. He addresses his patron as Theophilus, which means “one who loves God.” And this person may have wanted this work done so that he could distribute it. Luke also wrote Acts for the same patron.
John
ESV Global Study Bible - Intro to John
John’s gospel is different from the others. His audience seems to be everyone. He wanted everyone to “believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name.” John focuses more on the divine characteristics of Jesus and his being the Son of God.