This course is ideal for students and researchers seeking an introduction to First-order Modal Logic (FOML), providing foundational tools and insights to help understand its complexities. Attendees are expected to be familiar only with the basics of propositional modal logic. FOML extends propositional modal logic by introducing quantifiers, allowing for reasoning about necessity, possibility, and other modal concepts in a first-order setting. This enhances the expressiveness of modal logic, which creates a powerful tool for analysing multi-agent systems and reasoning about relationships between entities under varying conditions. Hence, FOML finds applications in philosophy, computer science, linguistics, mathematics and artificial intelligence. This course emphasises the semantic approach to FOML and explores practical methods for integrating quantifiers and modal operators within the same system. Attendees will gain foundational knowledge of the semantics and associated proof theories.