Fundamentals -- Advanced properties of topological spaces -- Basic algebraic topology -- Manifold theory -- Moore-Smith convergence and nets -- Function spaces -- Knot theory -- Graph theory -- Dynamical systems -- Appendix 1: Principles of logic -- Appendix 2: Principles of set theory -- Appendix 3: The real numbers -- Appendix 4: The axiom of choice and its implications -- Appendix 5: Ideas from algebra