Were greatly amazed - Were astonished and surprised at his sudden appearance among them.
Saluted him - Received him with the customary marks of affection and respect. It is probable that this was not by any "formal" manner of salutation, but by the "rush" of the multitude, and by hailing him as the Messiah.

Were greatly amazed - Probably, because he came so unexpectedly; but the cause of this amazement is not self-evident.

And straightway all the people, when they beheld him,.... As soon as ever they saw him, to many of whom, especially those that followed him out of Galilee, he was personally known.
Were greatly amazed; either that he should come at that juncture, to assist and relieve his disciples, when the Scribes were triumphing over them, as some think; or rather, as others, on account of that remaining lustre and glory which was on his countenance, through his transfiguration, and not yet wholly gone off; like that which was on the face of Moses, when he came down from Mount Sinai:
and running to him, saluted him; wishing him all peace and prosperity, expressing their great joy at his coming to them; which was very desirable by them, and exceedingly pleasing to them, and especially at this time, as both their words and gesture showed.

And straightway all the people--the multitude.
when they beheld him, were greatly amazed--were astounded.
and running to him saluted him--The singularly strong expression of surprise, the sudden arrest of the discussion,and the rush of the multitude towards Him, can be accounted for by nothing less than something amazing in His appearance. There can hardly be any doubt that His countenance still retained traces of His transfiguration-glory. (See Exodus 34:29-30). So BENGEL, DE WETTE, MEYER, TRENCH, ALFORD. No wonder, if this was the case, that they not only ran to Him, but saluted Him. Our Lord, however, takes no notice of what had attracted them, and probably it gradually faded away as He drew near; but addressing Himself to the scribes, He demands the subject of their discussion, ready to meet them where they had pressed hard upon His half-instructed and as yet timid apostles.

All the multitude seeing him were greatly amazed - At his coming so suddenly, so seasonably, so unexpectedly: perhaps also at some unusual rays of majesty and glory, which yet remained on his countenance.