Asset Liability Management (ALM) is an important tool used in the administration of banks, insurance companies and pension funds, especially for monitoring and controlling the risk those institutions usually face. Among the various types of risk, the interest rate risk is one of the main sources of potential loss for a financial institution. This dissertation aims to study ways of controlling this type of risk. Thus, we will thoroughly study the strategy used for Asset Liability Management. This strategy consists in assembling an optimum portfolio in a way that it becomes unaffected by changes in the interest rates. A couple of immunization models for fixed rate portfolios are studied in detail. One of them employs the method of principal component analysis (PCA), immunizing the portfolio in the direction of those components. The other model minimizes the stochastic risk. In both of them, we present an example and use of the method in a Brazilian pension fund (this strategy is highly interesting to pension funds since they work with a long liability cash flow and want to certify their obligations will always be satisfied). Finally, we analyse the results obtained with the two methods.