In this paper, foundations of the geometrical theory of distillation trajectory bundles at finite reflux are stated. The conditions of trajectories tearing off boundary elements of the concentration simplex and regularities of an arrangement of trajectories of reversible distillation and stationary points of bundles of trajectories at finite reflux are considered. The analysis of the joining of sectional trajectory bundles is carried out at minimum reflux ratio and reflux ratio above minimum. The established laws allow the development of algorithms of optimal synthesis of separation schemes and optimal designing of distillation columns.