Abstract: We follow Mazorchuk's lectures on \(sl_2(\mathbb{C})\)-modules. We begin with an overview of the lie algebra \(sl_2(\mathbb{C}) = g\) and \(g\)-modules. We then prove the classification of simple finite-dimensional \(g\)-modules. Using this classification, we discuss finite-dimensional modules in general by showing that they are always semi-simple. Given time, we end with an outline of what tensor products of these finite-dimensional modules look like.