The monograph summarizes the problem of risk for any type of natural phenomenon, defines each of the terms that intervene in the risk analysis, describes the way in which these terms interact and some of them are particularized for the case of the seismic phenomenon. A synthesis is made of the deterministic and probabilistic methods for the evaluation of the seismic hazard at regional and local scales. Then, the theoretical basis of the analytical methods for assessing seismic damage in buildings is explained. The hysteretic behavior of reinforced concrete elements is studied, the factors controlling this behavior and the main computational models are described. The different indicators used to estimate the damage in structural elements and globally in the structure are examined and the probabilistic interpretation of the analytical methods is explained. Next, we describe the subjective methods of damage prediction, such as those based on damage probability matrices or vulnerability functions, and we show the form taken by the specific risk equation in each of these two cases. A methodology for the evaluation of seismic vulnerability in urban areas is developed, based on the vulnerability index method; it is described how the vulnerability of a building is calculated and the existing vulnerability functions for the estimation of risk scenarios are shown. The problem of the seismic risk analysis at urban level is studied and an example of application of this methodology to a sector of Barcelona is shown. Finally, a procedure for the simulation of vulnerability functions for reinforced concrete buildings is described and vulnerability functions are obtained for different structural typologies and different degrees of seismic intensity.