Explore the fundamental concepts of algebraic topology in this advanced university lecture that introduces algebraic invariants of topological spaces. Begin by reviewing the fundamental group as a key algebraic invariant and examine its essential property of homotopy invariance. Discover how this concept extends to other important algebraic invariants including higher homotopy groups, homology, and cohomology groups. Learn how these mathematical tools provide powerful methods for distinguishing and classifying topological spaces through their algebraic properties. Gain insight into the theoretical framework that connects abstract algebra with geometric and topological structures, forming the foundation for advanced study in algebraic topology and its applications in modern mathematics.