This introductory course surveys various mathematical concepts utilised in financial economics. Together with Financial Econometrics, it constitutes the foundation of the ‘research’ pillar in MSc Financial Economics at ISM. As such, some of the topics will be ‘repeated’, but more in depth, in other courses. As clients’ profiles and objectives have become increasingly global and complex over the past few decades, financial institutions have come up with more sophisticated and more structured products, alternatives, and approaches, some of which are reviewed in this course from a pricing and mathematical perspective. Given the current political environments (e.g. transpacific trade war, COVID), we pay significant attention to the assumptions behind formulae and models, while we practice not only calculations but also explanations to prepare ourselves for the contemporary regulatory environment, most notably characterised by the MiFID II and SFDR.