The Sermon on the Mount is found in Matthew chapters 5, 6 and 7. It is the largest grouping of teachings of Jesus in the New Testament and gives the basic tenets of Christian behavior. Some of the more famous inclusions are the Beatitudes which are eight characteristics of good people and a result of having those characteristics in proverb-like proclamations. The eight characteristics are (i) poor in spirit, (ii) those who mourn, (iii) the meek, (iv) those who hunger and thirst for righteousness, (v) the merciful, (vi) the pure in heart, (vii) the peacemakers and (viii) those who are persecuted for righteousness' sake (Matt. 5:3-10). Another inclusion is what is kown as the Antitheses (Matt. 5:17-48) which reinterpret commandments in the Hebrew Bible and give them loftier, more difficult interpretations. For example, instead of an eye for an eye, one must turn the other cheek. Instead of not committing adultery, one must not look at a woman lustfully. The Lord's Prayer (Matt. 6:5-13) is another well-known inclusion.
The Sermon on the Plain, found in Luke 6:17-49, is similar to the Sermon on the Mount, but much shorter. Parts of the Sermon on the Mount not found in the Sermon on the Plain are found dispersed through other parts of Luke. An analysis of the differences between the Sermon on the Mount and the Sermon on the Plain is here. Some scholars believe they are the same sermon. Others believe the sermons happened at different times. That like people today who travel from city to city and preach the same sermon, Jesus was teaching variations of the same material to different people.
The location for the giving of the Sermon on the Mount is not certain. Matthew 5:1 says Jesus "went up on a mountainside and sat down" and began to teach. Matthew 4:23-25, right before that, has Jesus in Galilee. Luke 6 has Jesus in Capernaum, then Jesus goes "out to a mountainside to pray..." In the morning he calls his disciples and chooses 12 apostles, then he goes "down with them" and stands "on a level place" where a crowd of people has come to hear him. Then he gives the Sermon on the Plain. Right afterwards, he goes back to Capernaum. For those who believe the Sermon on the Mount and the Sermon on the Plain are the same sermon, they reconcile the location by finding a level place on a mountain or hill, just below the summit, near Capernaum, on the northwest shore of the Sea of Galilee. For example, see here.
I have found three suggested locations for the Sermon on the Mount and we visited two of them on our trip to Israel earlier this year. One location is known as Mt. Eremos, a hill located between Capernaum and Tabgha. In about 381, the Spanish pilgrim Egeria, speaking of the area where the the Church of the Multiplication of the Loaves and Fishes now is, said, "Near there on a mountain is a cave to which the Savior climbed and spoke the Beatitudes." A rock-cut cistern has been found on Mt. Eremos with the ruins of a small late 4th century church over it. Near it today is the Roman Catholic Church of the Beatitudes built between 1936 and 1938. It has an octagonal floor plan, each one of the eight sides representing one of the Beatitudes.
|Church of the Beatitudes.|
|The altar inside the Church of the Beatitudes.|
|Mosaic tiles in the church.|
|Mosaic tiles outside the Church of the Beatitudes.|
|The large grassy field below is believed by some to be where the Sermon on the Mount was given.|
|A view from Arbel Mountain looking down on Midgdal, Capernaum in the distance and the Sea of Galilee.|
|This painting of the Sermon on the Mount by James Tissot in 1890 appears to conceptualize the area of Arbel Mountain. From Wikipedia.|
|This is a view of Arbel Mountain (right of center) from Mt. Eremos.|
Other believers question whether the Sermon on the Mount took place at all. One of those is Professor Luke Timothy Johnson of Emory University, formerly a Benedictine monk. In the course "Jesus and the Gospels" for The Teaching Company, Part 2 of 3, pages 12 to 14, Professor Johnson says the Sermon on the Mount is "the invention and creation of Matthew,...not Jesus. Matthew has drawn from the Q material [a hypothetical written collection of Jesus's sayings], those saying materials and possibly the oral tradition, and has woven them together into the form of these discourses...[T]he same Q materials are distributed by Luke quite differently."