Risk being its raw material, insurance has developed various techniques of valuation and risk transfer. Nowadays, these techniques - and first of all reinsurance, the favourite way of transferring risk- are entirely reassessed considering the development of Corporate Finance theory. Therefore, the approach retained here, originally for the actuarial course at Ensae, Paris may surprise some readers and students as it proposes a extended view of risk. We cover not only the mathematical aspects of Risk Management but also other fields relevant for Risk Management from economy or finance. We aim here at making bridges between all these fields through practical application to catastrophe risk. This second edition has been simplified, corrected and updated significantly.