Algebraic topologists study the properties of spaces that are preserved under continuous transformations. They use algebraic methods to analyze topological spaces, focusing on concepts like homotopy, homology, and fundamental groups. This field connects algebra and topology, allowing mathematicians to classify and understand complex shapes and structures. By applying algebraic techniques, algebraic topologists can solve problems related to the shape and connectivity of spaces. Their work has applications in various areas, including data analysis, robotics, and physics, where understanding the underlying structure of data or physical systems is crucial for advancements in technology and science.