# Topics - Topological spaces: axioms, examples - Bases for a topology - Continuity - Order, product, subspace, metric, quotient topologies, - Topological groups - Closed sets and limit points - Connectedness, path-connectedness, local connectedness, etc. - Compactness, limit point compactness, sequential compactness, local compactness, etc. - Countability and separation axioms, normal spaces - Urysohn Metrization Theorem - Tychonoff's Theorem (statement only), compactification - Fundamental group - Covering spaces - Seifert-van Kampen - Classification of surfaces