The textbook provides an introduction to typical problems in modern financial mathematics. It presents the most important financial mathematical principles (arbitrage, duplication, diversification) and results (fundamental theorems of option pricing) within a simple discrete-time framework, without requiring the methods of continuous-time market models. Building on continuous-time modeling of financial markets, it then addresses the issues of option pricing (particularly the Black-Scholes formula) and portfolio optimization (optimal investment strategies). The necessary mathematical tools (such as Brownian motion, martingale theory, Itô calculus, stochastic control) are provided in independent excursions. Direct connections to practical applications in the financial industry are discussed in introductory sections through the presentation of popular topics.