The promised son, Isaac, is finally born when Abraham is 100 years old and Sarah is 90. After he is weaned, Sarah sees Ishmael mocking his little brother. She goes to Abraham and demands he send Hagar and Ishmael away. Abraham loves both his sons and does not know what to do so he asks God who tells him to grant his wife's wish. The next morning Abraham gives them bread and water and sends them away. They travel south (possibly going back to her home in Egypt) and make it to Beersheba. While wandering in the wilderness the water runs out. She knows Ishmael will die without water so she has him sit away from her so she doesn't have to watch it. However, she is close enough to try to protect him from people and animals and so that he won't feel deserted. God promised her before Ishmael was born that he would be the father of a great nation. Knowing that, she should have had faith that God would protect him, right? She had been through so much over the years and was forced out of her home so abruptly that she probably forgot His promise or she might have thought God had changed His mind. He calls to her and reminds her of His promise and shows her a well of water.
We need not fear when we are lost or when it seems that He has changed His mind. Our Father will never leave us nor forsake us. He always keeps His covenant with us.
Abimelech and Abraham make a pact that they will live peaceably together. One day, unbeknownst to Abimelech, his servants violently take away Abraham's well. Instead of starting a war Abraham meets with Abimelech and questions him about it. He denies any knowledge and they make another agreement.
This is a good example of how we should treat others. When someone wrongs us or we think they have, we should go to them and try to resolve it peaceably. Maybe they didn't know they were hurting you. We are to forgive no matter what the reason for the conflict or God won't forgive us. In Matthew 6:14-15 Jesus says: (14) For if ye forgive men their trespasses, your Heavenly Father will also forgive you: (15) But if ye forgive not men their trespasses, neither will your Father forgive your trespasses.