The introduction of the chapter discusses the well-known analogies between difference calculus and differential calculus, leading to the development of a higher-level calculus that encompasses both concepts. The authors propose a system of axioms, including the notion of a (strong) measure chain, to establish a generalized differential and integral calculus. Key examples such as \(\mathbf{R}\) and \(\mathbf{hZ}\) are highlighted, along with the concept of a measure chain for any closed subset of \(\mathbf{R}\). The chapter also explores specific examples, such as a modified population dynamics model from bio-mathematics, to illustrate how measure chain calculus can systematically handle dynamical equations over various time scales. The example demonstrates that differential equations with pulses can be described within the calculus on measure chains, provided strictly positive time gaps are considered between interval endpoints. The chapter concludes by emphasizing the versatility of measure chain calculus, which can handle even exotic time scales like the Cantor set. The authors aim to provide a foundational framework for the measure chain calculus, which can be extended to prove many theorems from the qualitative theory of dynamical systems.The introduction of the chapter discusses the well-known analogies between difference calculus and differential calculus, leading to the development of a higher-level calculus that encompasses both concepts. The authors propose a system of axioms, including the notion of a (strong) measure chain, to establish a generalized differential and integral calculus. Key examples such as \(\mathbf{R}\) and \(\mathbf{hZ}\) are highlighted, along with the concept of a measure chain for any closed subset of \(\mathbf{R}\). The chapter also explores specific examples, such as a modified population dynamics model from bio-mathematics, to illustrate how measure chain calculus can systematically handle dynamical equations over various time scales. The example demonstrates that differential equations with pulses can be described within the calculus on measure chains, provided strictly positive time gaps are considered between interval endpoints. The chapter concludes by emphasizing the versatility of measure chain calculus, which can handle even exotic time scales like the Cantor set. The authors aim to provide a foundational framework for the measure chain calculus, which can be extended to prove many theorems from the qualitative theory of dynamical systems.