This chapter presents the main results on existence, uniqueness and stability, first of the general equilibrium of pure exchange and then of the non-capitalistic general equilibrium of exchange and production. For the exchange economy, attention is given to problems raised by survival; two proofs of existence of equilibrium are explained. On uniqueness, the chapter illustrates the Sonnenschein–Mantel–Debreu result and criticizes the usefulness of the notion of regular economies; Hicks’s conviction that income effects largely neutralize one another is questioned with a graphical example. On stability, the chapter presents the proof of tâtonnement stability under the Weak Axiom holding for market demand, using the notion of Lyapunov stability. For the production economy, the chapter notes that the gross substitutes assumption does not guarantee uniqueness, that the tâtonnement encounters a problem that renders a planner–auctioneer indispensable and that a new cause of possible instability arises, self-intensive consumption: Harry Johnson’s attempt to minimize its likelihood is reported. Mandler’s proof of stability under the Weak Axiom is reported, but an observation by Hildenbrand and Grodal renders the Weak Axiom even more unlikely to hold in a production economy. The online Appendix completes the criticism of regular economies by supplying an example.