B is a method for specifying, designing and coding software systems. It is based on Zermelo-Fraenkel set theory with the axiom of choice, the concept of generalized substitution and on structuring mechanisms (machine, refinement, implementation). The concept of refinement is the key notion for developing B models of (software) systems in an incremental way. B models are accompanied by mathematical proofs that justify them. Proofs of B models convince the user (designer or specifier) that the (software) system is effectively correct. We provide a survey of the underlying logic of the B method and the semantic concepts related to the B method; we detail the B development process partially supported by the mechanical engine of the prover.