Orthogonal modular varieties are locally symmetric varieties associated to integral quadratic forms of signature (2,n). They are related to various branches of Mathematics such as Algebraic Geometry (especially as moduli spaces of K3 surfaces and hyperKahler manifolds), Number theory and Representation theory. In these lectures, I will give an introduction to the geometry of orthogonal modular varieties, with focus on the topics such as toroidal compactifications, Kodaira dimension and mixed Hodge structures.