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Quantitative analysis in determinig rational prices of financial derivatives is of key importance in Financial Mathematics. This book presents student and practitioners orientated introduction into this rapidly growing area. Our main objective is to introduce and apply the key principles of Financial Mathematics in a clear way. In particular, the Black-Scholes theory and more advanced multidimensional Lévy driven models are developed in details. This leads to practical approximation formulas to determine no-arbitrage option prices. The book can be considered as an inspirational source for practitioners, graduate and postgraduate students, MSc and PhD projects, to those working in Quantitative Finance and Economics.