How does Romans 11 explain the salvation of Israel?

In Romans 11, Paul addresses the question of whether God has cast away His people, Israel. He emphatically states that God has not rejected His people whom He foreknew. The chapter explains that while many Israelites have stumbled and not attained righteousness, there remains a remnant according to the election of grace. The verse 'All Israel shall be saved' signifies that God’s redemptive plan includes not just Gentiles but also His chosen people, the Jews. This assurance is rooted in God's covenantal promises and underscores the notion that His mercy extends to all whom He has chosen, providing a glimmer of hope for the fulfillment of His promises to Israel.