In this talk, we give a brief introduction to a natural generalization of groups, called n-groups. Just as discrete groups represent the homotopy types of acyclic spaces, n-groups realize homotopy types of connected topological spaces X such that $\pi_i(X)=0$ for $i>n$. In this talk, we adopt the formalism of simplicial sets, and define n-groups as simplicial sets satisfying certain a filling condition (introduced by Duskin).\\ In the first part of the talk, we explain what a 2-group look like: this material is contained in any textbook on simplicial sets. We indicate how 2-groups arise in topological quantum field theory.\\ In the second part of the talk, we explain a generalization of Lie theory to n-groups, in which the role of Lie algebras is taken by differential graded Lie algebras, and the role of the ordinary differential equations underlying Lie theory is taken by the Maurer-Cartan equation for flat superconnections on simplices.