This course introduces the basic theory of convex optimization and illustrates its practical employment in a wide range of FinTech applications. Techniques and applications of nonconvex optimization are also considered. Examples of the problems considered include Markowitz portfolio optimization and its many variations (e.g., maximum Sharpe ratio portfolio, risk-parity portfolio, robust portfolio, sparse portfolio), data fusion, machine learning for classification/estimation, imputation of missing data, big data analysis, outlier detection, data clustering, and deep learning.