1 After these things Jesus walked in Galilee: for he would not walk in Jewry, because the Jews sought to kill him.

[After these things] The apostle John passses from the preceeding discourse of our Lord, which he delivered a little before the passover, John 6:4, to the Feast of Tabernacles, which happened six months after, and thus omits many things mentioned by the other evangelists, which our Lord said and did during that time. He had already gone over Galilee four or five times; and he continued there, because he found that the hatred of the Jewish political and religious leaders was such that they would kill him if they could meet with him in Judea; and his time to suffer was not yet come.

[For he would not walk in Jewry] He was no longer tolerated, and could not preach publicly in Judea except at the risk of his life.
Geographical note. At the time of Jesus Israel was divided into three regions. The southern region was Judea, where Jerusalem was located and political/religious power was concentrated. These rulers had much to lose if Messiah came and excluded them from his anticipated new kingdom.
The middle region was Samaria, populated largly by partially Jewish mixed blood people, despised by the full-blooded Jews.
The northern region was Galilee, on the western shores of the Sea of Galilee. The populace was regarded by the Judean Jews as simple and uneducated.

2 Now the Jew's feast of tabernacles was at hand.

[Feast of Tabernacles] This feast was celebrated on the fifteenth day of the month Tisri, answering to the last half of our September and the first half of October. The feast took it's name from the tents which were erected about the temple, in public places, in courts, on the flat roofs of their houses and in gardens; in which the Jews dwelt for eight days in commemoration of the forty years during which their fathers dwelt in the wilderness. It was one of three solemn feasts in which all males were required, by law, to appear at Jerusalem.

3 His brethren therefore said unto him, Depart hence, and go into Judaea, that thy disciples also may see the works that thou doest.

[His brethren...said] Jesus was Mary's firstborn, while she was yet a virgin. Other brothers and sisters were born later. See Matthew 13:53-58.

[That thy disciples also may see] That is the disciples which he had made in his previous trips to Jerusalem.

4 For there is no man that doeth any thing in secret, and he himself seeketh to be known openly. If thou do these things, shew thyself to the world.
5 For neither did his brethren believe in him.

[Neither did his brethren believe in him] This was a mild challenge. You perform miracles and claim to be the Messiah here in Galilee, but let's see what happens when you make these claims in the "real world."

6 Then Jesus said unto them, My time is not yet come: but your time is alway ready.

[My time is not yet come] A theme repeated in the Gospels. See John 2:4, verses 6, 8 and 30 of this chapter, John 8:20 and culminating in John 17:1.

7 The world cannot hate you; but me it hateth, because I testify of it, that the works thereof are evil.

[The world cannot hate you] Because you are in agreement with it. You expect a political Messiah.

[But me it hateth] Because I condemn the ungodliness. Because my life and doctrine awaken guilt.

8 Go ye up unto this feast: I go not up yet unto this feast: for my time is not yet full come.
9 When he had said these words unto them, he abode still in Galilee.

[I go not up yet] Our Lord still had some business to attend to before going to the feast. We do not know what it was, but we know that time alone with the Father was a high priority.

10 But when his brethren were gone up, then went he also up unto the feast, not openly, but as it were in secret.

[But as it were in secret] His arrival at the feast was to be low key, without fanfare.

11 Then the Jews sought him at the feast, and said, Where is he?
12 And there was much murmuring among the people concerning him: for some said, He is a good man: others said, Nay; but he deceiveth the people.
13 Howbeit no man spake openly of him for fear of the Jews.