The paper concerns the existence of absolute embeddings \(e\) of point-line geometries \(\Gamma=({\mathcal P},{\mathcal L})\), that is, any embedding of \(\Gamma\) in some projective space can be derived from \(e\) by projecting onto suitable quotient spaces. Only a few point-line geometries like polar spaces of rank at least 2 were known to possess absolute embeddings. Apart from a method by \textit{A. L. Wells} [Q. J. Math., Oxf. II. Ser. 34, 375-386 (1983; Zbl 0537.51008)] and one by the second author [Coverings of graphs, Lecture Notes, Kansas State University 1997] no further methods were known for showing that a Lie incidence geometry which is not already a projective space or a polar space is absolutely embeddable. Furthermore, Wells' method has limited application (mostly for spin and half-spin geometries) whereas the second method involves a hypothesis (that the embeddable geometry possesses Veldkamp lines and that every geometric hyperplane arises from some fixed embedding) which is sometimes difficult to verify. In the paper under review the authors present a new inductive method. It involves a family \({\mathcal R}\) of connected subspaces of a point-line geometry \(\Gamma\) such that every subspace \(R\in{\mathcal R}\) contains a line, possesses an absolute embedding over the field \(k\) and such that every line lies in a member of \({\mathcal R}\). The authors then form a graph \(\Sigma\) with vertex set \({\mathcal R}\) and they make several technical assumptions on the intersection of members of \({\mathcal R}\) and certain subgraphs and they assume that \(\Sigma\) is simply connected. (In one case \(A,B\in {\mathcal R}\) are adjacent if and only if \(A\cap B\) is connected and contains a line.) If \(\Gamma\) is embeddable over \(k\), then it is shown that \(\Gamma\) has an absolute embedding. For the proof of the theorem the authors consider two embeddings over \(k\) of \(\Gamma\) and show that they yield isomorphic point-line presheaves. Then both embeddings possess the same universal hull. Hence all embeddings over \(k\) are derived from that hull so that this provides an absolute embedding. In the last section of the paper the authors apply their result to show that every embeddable Lie incidence geometry of sufficient rank possesses an absolute embedding.