Stable homotopy theory is a branch of algebraic topology that studies the properties of topological spaces through the lens of stable phenomena. It focuses on the behavior of spaces when they are "stabilized" by taking suspensions, which essentially means adding dimensions to the spaces. This allows mathematicians to analyze their homotopy groups in a more manageable way. In stable homotopy theory, one often uses tools like spectra, which are sequences of spaces that encode stable homotopy information. This theory has deep connections to other areas of mathematics, including category theory and cohomology, and plays a crucial role in understanding the relationships between different topological spaces.