Does God change?
Is God of the book of Genesis the same God of today?
My way of understanding it is that God's fundamental nature is described in words like love, mercy, compassion, justice, and forgiveness. Like the love of a parent, changing circumstances evoke different expressions of that love. Thus, the parent who simply held and fed the baby eventually walks beside the child, guides the teenager, gives wings to the young adult, and supports the older adult as needed. Every step of that journey seems different, and the child certainly develops in response to it, and yet it's fair to say that the original orientation to love the child has remained in force.
I don't see any sign that God has gone from love to hate, or from mercy to cruelty. In that sense, God seems constant. I do see signs that God's foundation for humankind, expressed perhaps as law, has changed over time. Certainly our understanding of it has changed. Thus, a social covenant that enabled Israel to cross the wilderness was changed later to a more inclusive, less tribal covenant under Jesus.
God's relationship to the global reach of humanity seems to have changed, too, as far as we can know that reach. In the early days, God worked through Israel as a “beacon to the nations.” Later, when Israel seemed unable to fulfill that role, God worked through Jesus of Nazareth and, in his followers, set in motion a new and farther-reaching community of faith. As time went on, God seemed to work beyond Christianity, by adding other expressions to humanity's journey, such as Islam.
Finally, throughout this journey, God has shown a willingness to suffer along with, and on behalf of, humanity. From betrayal in the Garden to death on the cross, and surely beyond, God has felt the pain that comes from loving another. I believe that suffering has changed God.