This chapter explains several kinds of risk measures that allow readers to quantify the risk of an investment portfolio. We are going to classify risk measures into two categories: based on their properties and based on the characteristic it quantifies. We are going to focus on risk measures which functional form is convex because this kind of risk measures have a global minimum and can be modeled as convex optimization problems. For modeling the risk measures, we are going to use Disciplined Convex Programming methodology that imposes a set of conventions that one must follow when constructing convex optimization programs.