ABC on IBC

This is a tutorial introducing basic concepts of Information-Based Complexity (IBC) with the emphasis on tractability of multivariate problems. IBC deals with the complexity of computing approximate solutions of continuous problems. No prior knowledge of IBC is required from the reader, however, some knowledge of basic concepts of functional analysis and measure theory will be very helpful. This text is based on tutorials delivered by the author during the workshop “IBC-Paris 2017: Information-Based Complexity, High-Dimensional Problems” in Paris, March 2017, and the mini-semester at the Erwin Schrödinger Institute “Information-Based Complexity and Tractability of Multivariate Problems” in Vienna, September–October 2017.