Point-set topology and introduction to algebraic topology
Introduction to sets, topological spaces, and basic definitions
Generating topologies and comparing different topological structures
Continuous functions and topological equivalence
Connected and path-connected spaces
Compact spaces and their fundamental properties
T0, T1, Hausdorff, and other separation properties
Metric topology and its relationship to general topology
Fundamental groups and basic homotopy theory
Comprehensive references and review materials