The course provides a glimpse into selected topics of current mathematical research interest. The aim is to familiarize participants with basic notions, problems, and results outside their own research area. Possible topics will be discussed at an information meeting in January. Selected topics from previous years include the Kadison-Singer problem, the discrete Kakeya problem, arithmetic progressions in the primes, the cut-off phenomenon in Markov chains, Schramm-Loewner evolution, and recent progress on sphere packing. The course format emphasizes interaction between students and active engagement.