This book constitutes the refereed proceedings of the 45th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2019, held in Nový Smokovec, Slovakia, in January 2019. The 34 full papers presented together with 6 invited talks were carefully reviewed and selected from 92 submissions. They presented new research results in the theory and practice of computer science in the each sub-area of SOFSEM 2019: Foundations of theoretical Computer Science, foundations of data science and engineering, and foundations of software engineering.