- Introduction.- 1. Topologies.- 2. Families of Subgroups.- 3. Free Products of Finitely Many Profinite Groups.- 4. Generalized Free Products.-5. Relative Embedding Problems.- 6. Strong Proper Projectivity.- 7. ?tale Profinite Subset of Subgr(G).- 8. Fundamental Result.- 9. Main Result. Bibliography.- Index.