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0 Elementary Facts.- 1 Homomorphisms, Prime Subgroups, Values and Structure Theorems.- 2 Lattice-Ordered Permutation Groups.- 3 Model Theory of Abelian l-Groups.- 4 Groups of Divisibility: A Unifying Concept for Integral Domains and Partially Ordered Groups.- 5 The Lattice of Convex l-Subgroups of a Lattice-Ordered Group.- 6 Torsion Theory of l-Groups.- 7 Completions of l-Groups.- 8 Characterization of Epimorphisms in Archimedean Lattice-Ordered Groups and Vector Lattices.- 9 Free Lattice-Ordered Groups.- 10 Varieties of Lattice-Ordered Groups Norman.- 11 Free Products in Varieties of Lattice-Ordered Groups.- 12 Amalgamations of Lattice-Ordered Groups.- 13 Generators and Relations in Lattice-Ordered Groups: Decision Problems and Embedding Theorems.