This dissertation addresses power system rare events (or major power system blackouts) comprehensively. It first proposes the use of cluster probability model to predict the long term tendency of cascading in power system. The proposed model successfully explains the distribution of existing observed statistics and gives a very well fit. The dissertation also proposes the use of the affinity index to evaluate the likelihood of power system multiple contingencies. In order to identify higher order contingencies, a systematic way is proposed to identify power system initiating contingencies (including higher-order). We use B-matrix to represent the connective of functional groups (also called protection control groups). It is the first to give the formula in matrix form to evaluate the probabilities of fault plus stuck breaker contingencies. The work extends the conventional contingency list by including a subset of high-order contingencies, which is identified through topology processing. The last part of this work also proposes the use of DET (dynamic event tree) as an operational defense tool to cascading events in power system. We tested our DET concept on a small system, which proved the effectiveness of DET as a decision support tool for control-room operator.