This paper explores compactifications of F-theory on Calabi–Yau threefolds and their relationship with heterotic string theories. It shows that N = 2 dualities between type II and heterotic strings in four dimensions become N = 1 dualities between heterotic and F-theory in six dimensions. The six-dimensional heterotic/heterotic duality is a geometric symmetry of the Calabi–Yau manifold in the F-theory setup. The paper also discusses the nature of the strong coupling transition and what lies beyond it in F-theory compactifications. The paper begins by introducing F-theory as a 12-dimensional formulation of type IIB strings. It discusses how F-theory compactifications can be viewed as compactifications on manifolds with elliptic fibrations. The paper then considers compactifications of F-theory on elliptic Calabi–Yau threefolds, which lead to N = 1 theories in six dimensions. It divides these into two classes: those with K3 fibrations and those without. The first class is studied in detail, while the second is discussed in a forthcoming paper. The paper then discusses heterotic compactifications on K3 and their duals in F-theory. It shows that the gauge group of the heterotic string can be determined by the instanton numbers of the gauge bundle. The paper also discusses the strong coupling problem in heterotic string compactifications and how F-theory compactifications shed light on this issue. The paper then discusses the mathematical aspects of elliptic Calabi–Yau threefolds, including their relation to the 7-brane worldvolume and the canonical bundle. It also discusses the construction of F-theory duals for heterotic string compactifications and the conditions for the existence of elliptic fibrations. The paper concludes by discussing the physical implications of the F-theory/heterotic duality, including the strong coupling phase transition and the heterotic/heterotic duality. It shows that the duality can be understood geometrically and that the phase transition can be studied using sigma model techniques. The paper also discusses the role of mirror symmetry in understanding the dualities and the implications for string compactifications.This paper explores compactifications of F-theory on Calabi–Yau threefolds and their relationship with heterotic string theories. It shows that N = 2 dualities between type II and heterotic strings in four dimensions become N = 1 dualities between heterotic and F-theory in six dimensions. The six-dimensional heterotic/heterotic duality is a geometric symmetry of the Calabi–Yau manifold in the F-theory setup. The paper also discusses the nature of the strong coupling transition and what lies beyond it in F-theory compactifications. The paper begins by introducing F-theory as a 12-dimensional formulation of type IIB strings. It discusses how F-theory compactifications can be viewed as compactifications on manifolds with elliptic fibrations. The paper then considers compactifications of F-theory on elliptic Calabi–Yau threefolds, which lead to N = 1 theories in six dimensions. It divides these into two classes: those with K3 fibrations and those without. The first class is studied in detail, while the second is discussed in a forthcoming paper. The paper then discusses heterotic compactifications on K3 and their duals in F-theory. It shows that the gauge group of the heterotic string can be determined by the instanton numbers of the gauge bundle. The paper also discusses the strong coupling problem in heterotic string compactifications and how F-theory compactifications shed light on this issue. The paper then discusses the mathematical aspects of elliptic Calabi–Yau threefolds, including their relation to the 7-brane worldvolume and the canonical bundle. It also discusses the construction of F-theory duals for heterotic string compactifications and the conditions for the existence of elliptic fibrations. The paper concludes by discussing the physical implications of the F-theory/heterotic duality, including the strong coupling phase transition and the heterotic/heterotic duality. It shows that the duality can be understood geometrically and that the phase transition can be studied using sigma model techniques. The paper also discusses the role of mirror symmetry in understanding the dualities and the implications for string compactifications.