This paper represents an important contribution to the subject of second order partial differential operators associated to non-commutative vector fields. The authors prove sharp subelliptic capacitary estimates for Carnot-Carathéodory rings associated to a family \(\{X_1, \dots, X_m\}\) of vector fields of Hörmander type. In this subelliptic context they also obtain a maximum principle for weak solutions of equations of the form \[ \sum^m_{j=1} X^*_jA_j(x,u,Xu) =f(x,u,Xu) \] with appropriate conditions on the functions \(A_j\) and \(f\). The authors extend classical results on removability of singularities for solutions of quasilinear elliptic equations to results on removability of singularities for weak solutions of this equation. All these results conduce to the core of the paper, which is to describe the local behavior of singular solutions of the equation above. In spite of their difficulty, the results are masterfully presented. The authors take great care to convey to the reader the important ideas and the connections with other results and applications. In particular, the authors dedicate an introductory section to motivate their results by presenting explicit fundamental solutions for the model equation \[ \sum^m_{j=1} X^*_j\bigl(|Xu |^{p-2} X_ju\bigr)=0 \] in the context of Heisenberg type groups.