Introduction to Mirror Symmetry in Geometry

Mirror symmetry bridges two seemingly unrelated branches of mathematics, transforming how we understand symplectic and complex geometry. This text-only course demystifies these deep geometric relationships, guiding you through the essential concepts without requiring years of advanced study. You will start with foundational definitions and key terminology before exploring how these mathematical dualities operate in modern geometry. Through clear, step-by-step written explanations, you will build a solid intuitive and theoretical groundwork in this fascinating field. What you will learn: Understand the core principles of complex and symplectic manifolds; Learn how mirror symmetry connects different geometric structures; Explore the basic formulations of homological mirror symmetry; Practice analyzing geometric dualities through structured written exercises; Discover modern geometric workflows and current theoretical developments in the field. This course begins with the absolute essentials, defining key terminology and basic concepts before moving into structural geometric relationships. It is designed for students, researchers, and mathematics enthusiasts who want a clear, accessible introduction to mirror symmetry without complex prerequisites. Start reading today to unlock a deeper understanding of modern geometric dualities.