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Metric and Topological Spaces
First part of this course note presents a rapid overview of metric spaces to set the scene for the main topic of topological spaces.Further it covers metric spaces, Continuity and open sets for metric spaces, Closed sets for metric spaces, Topological spaces, Interior and closure, More on topological structures, Hausdorff spaces and Compactness.
Author(s): T. W. Korner
102 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
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