Matthew seems to have Jewish readers particularly in mind, and begins with a genealogy of Jesus back to Abraham--showing Jesus as Legal Heir to the Promises given Abraham and David. In 1:23 Matthew quotes Isaiah 7:14, "...the virgin will be with child and will give birth to a son, and will call him Immanuel (which means 'God with us')."
Matthew is full of quotes from the Old Testament. See, for example: 2:15, 17-18 & 23; 3:3; 4:4, 6, 7, 10 & 16
In chapter 5 Jesus begins his public ministry with the Beatitudes (5:3-12). You are to Preserve & Guide (5:13-16). In verse 17 he says, "Do not think I have come to abolish the Law or the Prophets..." Pay particular attention to 5:17-20. In 5:21-7:27 Jesus expands and clarifies the law!
Chapter 13 contains parables (stories) of the Kingdom of Heaven. Herod, John the Baptist, the disciples and the people in general were expecting Jesus to rule a political kingdom similar to the kingdoms of their day. Jesus' kingdom is different. Laws, rules and control are important, but Jesus' kingdom is based on love--not duty. Love causes a person to want to do good and to enthusiastically seek ways to do even better. Law causes a person to grudgingly do what is required, always looking for loop holes...a way around the law. Jesus' Kingdom, based on LOVE, is a concept that seems logical but seems to be as difficult for us to put into practice today as it was nearly 2000 years ago.
Other parables of the Kingdom of Heaven are spread out throughout the book. Pay particular attention to the Greatest Commandment (22:34-40).
Jesus didn't abolish the Law or Prophets, he came to fulfill them - Matthew 5:17. The fulfillment is a new law, "...Love one another. As I have loved you..." (John 13:34). "...he who loves his fellow man has fulfilled the law." (Romans 13:8; also see James 2:8). Love causes a person to want to do good and to enthusiastically seek ways to do even better.