Although Luke says here that Jesus goes down the mountain and Matthew 5:1 says that he went up the mountain, there is no contradiction because Luke says in Luke 6:12 that Jesus went up the mountain to pray. That Jesus came down from the mountain in Luke 6:17 therefor means that he goes down for a little while and then stops where it is more level. It is important to note that this is the same place (see Matthew 28:16–20) where Jesus said the things that remain of great importance to the church of all ages: He has all authority in heaven and on earth, he gives missionary, baptismal orders, and orders to teach, and promises to be always with his church.
Luke distinguishes three categories of people: the twelve disciples with whom Jesus descends to the level ground, a large number of disciples who are already there, and a multitude of people from various places.
17 And he came down with them and stood on a level place, with a great crowd of his disciples and a great multitude of people from all Judea and Jerusalem and the seacoast of Tyre and Sidon,