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Basic topology
This note will mainly be concered with the study of topological spaces. Topics covered includes: Set theory and logic, Topological spaces, Homeomorphisms and distinguishability, Connectedness, Compactness and sequential compactness, Separation and countability axioms.
Author(s): Soren Fuglede Jorgensen
93 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 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
This PDF covers the following topics related to Topology : Topology of Metric Spaces, Topological Spaces, Basis for a Topology, Topology Generated by a Basis, Infinitude of Prime Numbers, Product Topology, Subspace Topology, Closed Sets, Hausdorff Spaces, and Closure of a Set, Continuous Functions, A Theorem of Volterra Vito, Homeomorphisms, Product, Box, and Uniform Topologies, Compact Spaces, Quotient Topology, Connected and Path-connected Spaces, Compactness Revisited, Countability Axioms, Separation Axioms, Tychonoff’s Theorem.
Author(s): IIT Kanpur
37 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