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In S. Michael’s answer, he cites Isaiah 42:8 in which Jehovah God states He will not give His glory to any other. May I suggest the intended meaning was that Jehovah God would not relinquish His deity to any other being, just as He would not give praise to graven images, for He is God Almighty and there is none like Him. I say this because we find, in John 17:22-23, the Lord giving the Father’s glory to those whom the Father chose for salvation.
From the same passage we see that God’s glory is in us, in the Father, and in the Lord, making us all one, that we should be made perfect. The Holy Spirit is in us from the moment we believe, confess our sins, and are baptized in Him. Does that make us perfect? Obviously not, but we are commanded by Jesus to be perfect (Matthew 5:48). What, then, can make us perfect?
Surely, it is God who works in us to perfect us (1 Peter 5:10), but it is the love of God that is perfected in us (1 John 2:5). And we know that God is agape love (1 John 4:8). It is God’s agape love that is in us, making us one, taking us back to John 17:25-26, to see that God’s glory is His agape love that is given to us. Thus, from John 17:22-26 we see that God’s Holy Spirit is equated to His agape love, and from 1 John 4:17-18, once agape love is perfected, it casts out fear – the fear of death. Oh Death, where is your sting? Oh Hades, where is your victory? We see that this happens when we put on immortality in 1 Corinthians 15:54-55.
God’s glory is His agape love. It is also His divine nature. What is the nature of agape love? That, of course, is defined in 1 Corinthians 13:4-7, but there is a progression in the life of a believer that leads to agape love. From 2 Peter 1:2-3 we see that to those who received a faith in Jesus, Peter wishes grace and peace would increase through the knowledge of God who called us to His glory and excellence. It is by God’s promises that we might become partakers of His divine nature (2 Peter 1:4). Diligence and moral excellence lead to knowledge (2 Peter 1:5 NASB). Perseverance and self-control lead to godliness (2 Peter 1:6 NASB), and brotherly kindness leads to agape love (2 Peter 1:7 NASB).
Apart from agape love, what else is there that can help us understand God’s glory, His divine nature? From Hebrews 6:18 we know that it is impossible for God to lie. This is an attribute that we will be able to lay claim to, after the resurrection, when we are in our glorified bodies. And James 1:13 tells us that it is impossible for God to be tempted by evil. These are the attributes of God’s divine nature, His glory that resides in the agape love that is in us to make us all one with the Father.