This course is an introduction to Yangians and their representation theory. Yangian of a simple Lie algebra g is a Hopf algebra deformation of the universal enveloping of the current algebra g[t], historically one of the first examples of quantum groups. Such Hopf algebras naturally arise in many different areas, from the Representation Theory of classical Lie algebras to Quantum Integrable Systems, Algebraic and Symplectic Geometry (in particular, in the phenomenon of symplectic duality), and Algebraic Combinatorics. We will start with some motivating examples coming from classical Representation Theory (Gelfand-Tsetlin bases and Olshansky centralizer construction), then develop the general theory of Yangians and their representations, and finally discuss some applications to Integrable Systems, Geometry, and Combinatorics.