This project is done with Dr. Celia Hacker and Dr. Stefania Ebli. We implement a framework for working with parametric Morse theory, which provides tools for analyzing the topological changes of a simplicial (cubical) complex through a filtration. One can build a discrete Morse function on a given complex (a real-valued labeling of all simplices or cubes that satisfies some hierarchy conditions) and study the related so-called critical cells in the complex. Those are crucial cells in the sense that, as opposed to other cells, deleting them from the complex will fundamentally change the overall topology of the space. DMT has applications in computational geometry and image processing.