Lecture I: Introduction to Nakajima quiver varieties Nakajima’s quiver varieties constitute a concrete but very important class of symplectic algebraic varieties. I will give a gentle introduction to the construction of quiver varieties and some basic geometric features, discuss examples, and briefly sketch their central place in geometric representation theory, enumerative geometry, and supersymmetric field theories of the last 20 years. If time permits, I will also place quiver varieties in a broader context of moduli spaces in symplectic algebraic geometry.