Digital markets form an increasingly important component of the global economy. The Internet has enabled new markets with previously unknown features (e-commerce, web-based advertisement, viral marketing, sharing economy, real-time trading), and algorithms play a central role in many decision processes involved in these markets. For example, algorithms run electronic auctions, adjust prices dynamically, trade stocks, harvest big data to decide market strat egies and to provide recommendations to customers. The focus of the proposal ALGADIMAR is on the development of new methods and tools in research areas that are critical to the understanding of digital markets: algorithmic game theory, market and me chanism design, machine learning, algorithmic data analysis, optimization in strategic settings. We plan to apply these methods so as to solve fundamental algorithmic problems motivated by Internet advertisement, sharing economy, mechanism design for social good, security games. While our research is focused on foundational work — with rigorous design and analysis of algorithms, mechanisms and games — it will also include empirical validation on large-scale datasets from real-world applications.