The Sermon on the Mount, given by Jesus after he choose his twelve disciples, are the beginning words of God's New Covenant (agreement) offered to all mankind. Unlike the Old Covenant, which offered only physical blessings, the New Covenant makes possible eternal spiritual blessings. Jesus likely choose to give his message from a hill so that as many people as possible could hear what he had to say.
The Bible is silent in regard to the exact location Jesus used to give his well-known message about the basic principles for living life (Matthew 5 - 7, Luke 6:20 - 49). The first part of Jesus' message, Matthew 5:3 - 12, is commonly referred to as the Beatitudes. As such, the location where he gave his entire message is sometimes called the Mount of Beatitudes.
The location, historically, where it is believed Jesus gave his sermon is called Mount Eremos, which has been commemorated as the place of his message for more than 1,5000 years. This mount is positioned on Galilee's northwest shore between the cities of Gennesaret and Capernaum. In the 4th century A.D. a Byzantine church structure was placed near this mount. The only things that remain from this building are pieces of a cistern and monastery. During the third Crusade in 1187 A.D., the great military leader Saladin and his Moslem forces completly defeated the crusaders at the mount. This victory compelled him to take the city of Jerusalem in October of the same year. In 1938 A.D. the Roman Catholic Church built a chapel near the famed mount.
The Mount itself overlooks the plain of Gennesaret, an area known for its fertility. The New Testament records several times that Jesus was in this area, including when he healed the multitudes and faced condemnation from the Pharisees for ritual impurity.
Jesus, after he and his disciples sat down (near the top of the ridge in the above photo where the church is located), began to give his "sermon" about simple but profound spiritual truths. Some of these were the value of being humble, merciful, a peacemaker and not returning evil to someone who sins against you.