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Introduction to Topology by Professor Denis Auroux
This note covers the following topics: Topological Spaces, Bases, Subspaces, Products, Continuity, Continuity, Homeomorphisms, Limit Points, Sequences, Limits, Products, Connectedness, Path Connectedness, Compactness, Uncountability, Metric Spaces,Countability, Separability, and Normal Spaces.
Author(s): Professor Denis Auroux
113 Pages 
Lecture notes on Topology by Huynh Quang Vu
This note covers general topology, Geometric topology and differential topology.
Author(s): Huynh Quang Vu
118 Pages
General Topology lecture notes
This note covers introduction, Set theory, Topological spaces, Metric topologies, Connected spaces, Compactness, Advanced material.
Author(s): Thomas Baird
59 Pages
General Topology by Paul Souverains
This note covers topological spaces, Continuous functions, Compact topological spaces, Compact metric spaces, Separability axioms and theorems, Metrizations.
Author(s): Paul Souverains
323 Pages
General Topology by Tom Leinster
This note covers the following topics: Topological spaces, metric spaces, Topological properties, Subspaces, Compactness, Compact metric spaces, Connectedness, Connected subsets of the real line.
Author(s): Tom Leinster
85 Pages