Linear Geometry: completions and projectivizations

Linear Geometry describes geometric properties that depend on the fundamental notion of a line. In this paper we survey basic notions and results related to completions and free projectivizations of liners.   The paper is the second survey in the series of surveys that describe the contents of the monograph ``Linear Geometry and Algebra'' [1]. The first survey [2] concentrated at properties of liners that depend on flat hulls (flats, ranks, regularity, parallelity). In this paper we survey basic notions and results related to completions and free projectivizations of liners. The material covers Chapters 7, 8, 9 of the book [1].