For the reader’s convenience, this chapter contains a review of basic concepts and results that are frequently used throughout the book: inverse systems and inverse limits; profinite spaces and profinite groups; profinite free groups; free and amalgamated products; profinite rings and modules; the complete group algebra and complete tensor product; Ext and Tor functors; homology and cohomology of profinite groups; cohomological dimension and homological characterization of projective profinite groups and free pro- p groups. This chapter does not contain proofs. These can be found, for example, in the monograph ‘Profinite Groups’ by L. Ribes and P. Zalesskii, 2nd edition, Springer 2010, which is cited as RZ in the book.