On foliations with transverse linear connection

The subject of this article is a review of the results on foliations with transversal linear connection obtained by the author together with N.I. Zhukova, and their comparison with the results of other authors. The work consists of three parts. The first part focuses on automorphism groups of foliations with a transversal linear connection in the category of foliations. In the second part the equivalence of the concepts of completeness for the class of foliations under investigation is studied. In the third part we present theorems on pseudo-Riemannian foliations that form an important class of foliations with a transversal linear connection. In particular, we present results on graphs of pseudo-Riemannian foliations that contain all information about foliations.