The Book of Matthew is one of four books that sets forth the four-fold
earthly-life and death and resurrection of the Lord Jesus Christ.
Matthew does not contain everything that Jesus said and/or did. Matthew
emphasizes the Lord Jesus Christ being God's appointed king, and refers
to God's kingdom as the kingdom of heaven.
This book was written after the resurrection and ascension of the Lord
Jesus Christ into heaven and after the out-pouring of holy spirit on the
day of Pentecost (Acts 2). Matthew wrote it by revelation – he received
the information of what to write via his holy spirit-life (not from his
intellectual memory).