Higher-dimensional geometry extends the principles of traditional geometry into dimensions beyond the familiar three. While we can easily visualize points, lines, and shapes in one, two, and three dimensions, higher dimensions involve additional axes that are not directly observable. For example, a four-dimensional object, like a tesseract, can be thought of as a cube extended into a new direction. In higher-dimensional spaces, mathematicians study properties such as distance, angles, and volume, which can be generalized from lower dimensions. This field has applications in various areas, including physics, computer science, and data analysis, where complex relationships and structures can be better understood through higher-dimensional models.