The Research Group in Nonlinear Algebra of Bernd Sturmfels at MPI-MiS Leipzig works on fundamental questions in algebra, geometry, and combinatorics. It advances and provides powerful tools to tackle problems in the sciences. Topics include algebraic statistics, combinatorial geometry, convex geometry, D-modules, numerical algebraic geometry, polynomial optimization, real algebraic geometry, tensor methods, and topological data analysis. In contrast to linear algebra, nonlinear algebra is yet underrepresented in applications. Some applications of nonlinear algebra in the sciences and engineering are showcased in the article “Nonlinear Algebra and Applications”.