Mirror Symmetry is a phenomenon first observed to occur in High-energy Theoretical Physics. Since the early 90s, mirror symmetry has been used to solve difficult mathematical problems known as curve-counting or enumerative questions in Algebraic Geometry. In his 1994 ICM address, Kontsevich proposed that mediating the rich geometry of Mirror Symmetry was abstract foundational mathematics which amounts to a categorical equivalence. From this sprang the conjecture of Homological Mirror Symmetry (HMS). HMS views two very different areas of mathematics, Symplectic Geometry and Algebraic Geometry, as opposite sides of the same categorical coin. Today, HMS is the cornerstone of an extremely active research field, reaching in influence far beyond its original formulation as a duality between Calabi-Yau manifolds, to such subjects as representation theory, singularity theory, and knot theory. At the core of the HMS research community are three different groups of researchers: algebraic geometers, symplectic geometers, and mathematical physicists. This thematic period will focus on  teaching young researchers all aspects of the field. This 6-month thematic period will consist of algebraic geometers, symplectic geometers, and mathematical physicists from around the world focusing on the most modern aspects of HMS with an emphasis on engagement with students and young researchers.