Risk measures play an extremely important role in the financial world as they enable the management and control of risks by quantifying them. In this paper, we have introduced some desirable properties of risk measures and described what a coherent risk measure would be. Measures of dispersion that we presented are the variance, the mean abolute deviation as well as the semi-interquartile range. Furthermore, we explained the Modern Portfolio Theory, presented the capital allocation line along with an efficient frontier and supporting this, used a Sharpe ratio to find the best portfolio on efficient frontier. The downside risk measures that we have introduced are SFRatio, semi-variance and Sortino ratio. We have introduced the Omega measure, which includes higher moments in the calculation and thus provides a complete characterization of returns and risks. In the second part of this paper, we defined Value at risk (VaR), one of the most well-known risk measures, and derived a formula for calculating VaR when returns are normally distributed. As an upgrade of the VaR methodology, we defined the Expected Shortfall. Also, we described the square root of time rule used to model risk with a holding period longer than one day. Marginal VaR, Component VaR and Incremental VaR are used to describe the contribution of individual positions to the total risk of the portfolio. Finally, a CoVaR measure is described, which identifies the risk of individual institutions that have an impact on market-wide risk.