This paper presents a unified approach to continuous and discrete calculus through the concept of measure chains. The author introduces a general calculus that encompasses both difference calculus and differential calculus as special cases. The key idea is the notion of a (strong) measure chain, which is a closed subset of the real numbers that can be used as a time scale for dynamic equations. The paper shows that any closed subset of R naturally forms a measure chain, and provides examples such as the set of integers, discrete subsets of R, and a specific measure chain P derived from a population dynamics model. The paper discusses a model of population dynamics where the population evolves according to a logistic differential equation, and then transitions to a discrete model with variable step size. It demonstrates that the measure chain calculus can systematically handle such models. The author also notes that even complex time scales like the Cantor set can be incorporated into the measure chain calculus, illustrating its flexibility. The paper emphasizes that the measure chain calculus provides a unified framework for both continuous and discrete calculus, allowing for the systematic development of theories of dynamic equations on various time scales. It avoids the need for separate treatments of discrete and continuous cases, and highlights the potential for extending the calculus in many directions. The paper also mentions that many theorems from the qualitative theory of dynamical systems can be proved within the general context of measure chain calculus. The author concludes by discussing the concept of conditionally complete chains, which is a key component of the measure chain calculus.This paper presents a unified approach to continuous and discrete calculus through the concept of measure chains. The author introduces a general calculus that encompasses both difference calculus and differential calculus as special cases. The key idea is the notion of a (strong) measure chain, which is a closed subset of the real numbers that can be used as a time scale for dynamic equations. The paper shows that any closed subset of R naturally forms a measure chain, and provides examples such as the set of integers, discrete subsets of R, and a specific measure chain P derived from a population dynamics model. The paper discusses a model of population dynamics where the population evolves according to a logistic differential equation, and then transitions to a discrete model with variable step size. It demonstrates that the measure chain calculus can systematically handle such models. The author also notes that even complex time scales like the Cantor set can be incorporated into the measure chain calculus, illustrating its flexibility. The paper emphasizes that the measure chain calculus provides a unified framework for both continuous and discrete calculus, allowing for the systematic development of theories of dynamic equations on various time scales. It avoids the need for separate treatments of discrete and continuous cases, and highlights the potential for extending the calculus in many directions. The paper also mentions that many theorems from the qualitative theory of dynamical systems can be proved within the general context of measure chain calculus. The author concludes by discussing the concept of conditionally complete chains, which is a key component of the measure chain calculus.