This article by Edward Witten explores the strong coupling dynamics of string theories in dimensions $d \geq 4$, focusing on the relationships between different string theories and eleven-dimensional supergravity. Witten argues that eleven-dimensional supergravity arises as a low energy limit of the ten-dimensional Type IIA superstring and that a conjectured duality between the heterotic string and Type IIA superstrings controls the strong coupling dynamics of the heterotic string in five, six, and seven dimensions. This duality implies $S$-duality for both heterotic and Type II strings. The paper begins by discussing the importance of understanding string theories in terms of their strong coupling behavior, which can provide clues for a new formulation of string theory. Witten notes that while there is strong evidence for $S$-duality in supersymmetric field theories, the evidence for $S$-duality in string theory is less extensive. He aims to improve this situation by analyzing the strong coupling behavior of string theories in various dimensions. In section two, Witten studies the strong coupling dynamics of Type II superstrings in ten dimensions, focusing on Type IIB. He discusses the $SL(2,\mathbf{Z})$ symmetry of Type IIB supergravity and its implications for the dynamics of the theory in lower dimensions. He also explores the role of $U$-duality in relating the dynamics of Type II theories in different dimensions. In section three, Witten considers the strong coupling dynamics of Type II theories below ten dimensions, emphasizing the role of $U$-duality in connecting different string theories. He discusses how the moduli space of vacua of Type II supergravity in $d$ dimensions has the form $G/K$, where $G$ is a non-compact connected Lie group and $K$ is a compact subgroup. He also explores the implications of $U$-duality for the dynamics of the theory. In section four, Witten analyzes the strong coupling limit of the five-dimensional heterotic string theory, finding that it is equivalent to Type IIB in six dimensions, and the strong coupling limit of the six-dimensional heterotic string theory is equivalent to Type IIA in six dimensions. He also discusses the strong coupling limit of the seven-dimensional heterotic string theory, which involves eleven-dimensional supergravity. These results are based on a relation between the heterotic string and the Type IIA superstring in six dimensions. In section five, Witten considers the strong coupling dynamics of the heterotic string in nine and eight dimensions, conjecturing that the strong coupling limit of the heterotic string in ten dimensions with $SO(32)$ gauge group might be the $SO(32)$ Type I theory. He shows that this relation, if valid, determines the strong coupling behavior of the heterotic string in nine and eight dimensions as well as ten. The paper concludes by discussing the possible relations between different string theories, noting thatThis article by Edward Witten explores the strong coupling dynamics of string theories in dimensions $d \geq 4$, focusing on the relationships between different string theories and eleven-dimensional supergravity. Witten argues that eleven-dimensional supergravity arises as a low energy limit of the ten-dimensional Type IIA superstring and that a conjectured duality between the heterotic string and Type IIA superstrings controls the strong coupling dynamics of the heterotic string in five, six, and seven dimensions. This duality implies $S$-duality for both heterotic and Type II strings. The paper begins by discussing the importance of understanding string theories in terms of their strong coupling behavior, which can provide clues for a new formulation of string theory. Witten notes that while there is strong evidence for $S$-duality in supersymmetric field theories, the evidence for $S$-duality in string theory is less extensive. He aims to improve this situation by analyzing the strong coupling behavior of string theories in various dimensions. In section two, Witten studies the strong coupling dynamics of Type II superstrings in ten dimensions, focusing on Type IIB. He discusses the $SL(2,\mathbf{Z})$ symmetry of Type IIB supergravity and its implications for the dynamics of the theory in lower dimensions. He also explores the role of $U$-duality in relating the dynamics of Type II theories in different dimensions. In section three, Witten considers the strong coupling dynamics of Type II theories below ten dimensions, emphasizing the role of $U$-duality in connecting different string theories. He discusses how the moduli space of vacua of Type II supergravity in $d$ dimensions has the form $G/K$, where $G$ is a non-compact connected Lie group and $K$ is a compact subgroup. He also explores the implications of $U$-duality for the dynamics of the theory. In section four, Witten analyzes the strong coupling limit of the five-dimensional heterotic string theory, finding that it is equivalent to Type IIB in six dimensions, and the strong coupling limit of the six-dimensional heterotic string theory is equivalent to Type IIA in six dimensions. He also discusses the strong coupling limit of the seven-dimensional heterotic string theory, which involves eleven-dimensional supergravity. These results are based on a relation between the heterotic string and the Type IIA superstring in six dimensions. In section five, Witten considers the strong coupling dynamics of the heterotic string in nine and eight dimensions, conjecturing that the strong coupling limit of the heterotic string in ten dimensions with $SO(32)$ gauge group might be the $SO(32)$ Type I theory. He shows that this relation, if valid, determines the strong coupling behavior of the heterotic string in nine and eight dimensions as well as ten. The paper concludes by discussing the possible relations between different string theories, noting that