This LNCS volume constitutes the proceedings of the First International Symposium on AI Verification, SAIV 2024, in Montreal, QC, Canada, during July 2024. The scope of the topics was broadly categorized into two groups. The first group, formal methods for artificial intelligence, comprised: formal specifications for systems with AI components; formal methods for analyzing systems with AI components; formal synthesis methods of AI components; testing approaches for systems with AI components; statistical approaches for analyzing systems with AI components; and approaches for enhancing the explainability of systems with AI components. The second group, artificial intelligence for formal methods, comprised: AI methods for formal verification; AI methods for formal synthesis; AI methods for safe control; and AI methods for falsification.