In topology, a smooth manifold is an object with the local appearance of familiar, flat space which may have interesting global properties. The surface of a ball or donut are typical examples of two-dimensional smooth manifolds. Contact manifolds carry additional geometric structure which make them especially useful for modeling physical phenomena. The unifying goal of this research project is to apply ideas from Morse theory, a powerful tool used in the study of smooth manifolds, to contact manifolds. This project will help to clarify the foundations of higher-dimensional contact topology, opening the door to further breakthroughs in this quickly developing field. In lower dimensions, software will be developed which carries out data science-style computations for knots in contact manifolds, and this software will be used to generate datasets which lead to further investigation. Importantly, the project will involve undergraduate students in meaningful mathematical research. This project has two parts, each falling under the general theme of Morse theory in contact topology. The first goal is to rigorously establish the bypass-bifurcation correspondence in higher dimensions. Contact topology in dimension 3 has seen enormous progress in the last quarter century, the vast majority of it through the use of convex surface theory. A fundamental tool in that dimension is the bypass, which discretizes the failure of convexity for 1-parameter families of surfaces. Hond