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Introduction to Topology University of California
This note covers the following topics: Basic set theory, Products, relations and functions, Cardinal numbers, The real number system, Metric and topological spaces, Spaces with special properties, Function spaces, Constructions on spaces, Spaces with additional properties, Topological groups, Stereographic projection and inverse geometry.
Author(s): University of California, Riverside
156 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
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
This PDF covers the following topics related to Topology : Preliminaries, Metric Spaces, Topological Spaces, Constructing Topologies, Closed Sets and Limit Points, Continuous Functions, Product and Metric Topologies, Connected Spaces, Compact Spaces, Separation Axioms, Countability Properties, Regular and Normal Spaces.
Author(s): Ali Sait Demir
64 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