Juan Maldacena discusses the large N limit of certain conformal field theories in various dimensions, showing that their Hilbert space includes a sector describing supergravity on Anti-deSitter (AdS) spacetimes, spheres, and other compact manifolds. This is demonstrated by considering branes in M/string theory and taking a low-energy limit where the field theory on the brane decouples from the bulk. The near-horizon geometry, which has enhanced supersymmetries, is trusted in this limit. The 't Hooft limit of 3+1 N = 4 super-Yang-Mills at the conformal point is shown to contain IIB strings. Maldacena conjectures that compactifications of M/string theory on various AdS spacetimes are dual to various conformal field theories, leading to a new proposal for a definition of M-theory that could include five non-compact dimensions. The paper explores this idea in detail for different cases, including D3 branes, M5 and M2 brane theories, and theories with lower supersymmetry, such as the D1+D5 system and black strings in five dimensions. The discussion also touches on the relation to matrix theory and the interpretation of the large N limit in non-conformal field theories.Juan Maldacena discusses the large N limit of certain conformal field theories in various dimensions, showing that their Hilbert space includes a sector describing supergravity on Anti-deSitter (AdS) spacetimes, spheres, and other compact manifolds. This is demonstrated by considering branes in M/string theory and taking a low-energy limit where the field theory on the brane decouples from the bulk. The near-horizon geometry, which has enhanced supersymmetries, is trusted in this limit. The 't Hooft limit of 3+1 N = 4 super-Yang-Mills at the conformal point is shown to contain IIB strings. Maldacena conjectures that compactifications of M/string theory on various AdS spacetimes are dual to various conformal field theories, leading to a new proposal for a definition of M-theory that could include five non-compact dimensions. The paper explores this idea in detail for different cases, including D3 branes, M5 and M2 brane theories, and theories with lower supersymmetry, such as the D1+D5 system and black strings in five dimensions. The discussion also touches on the relation to matrix theory and the interpretation of the large N limit in non-conformal field theories.