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Topology for the working mathematician
This note covers the following topics: Basic notions of point-set topology, Metric spaces: Completeness and its applications, Convergence and continuity, New spaces from old, Stronger separation axioms and their uses, Connectedness. Steps towards algebraic topology, Paths in topological and metric spaces, Homotopy.
Author(s): Michael Muger
407 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
Introduction to Topology by Alex Kuronya
This note covers Basic concepts, Constructing topologies, Connectedness, Separation axioms and the Hausdorff property, Compactness and its relatives, Quotient spaces, Homotopy, The fundamental group and some applications, Covering spaces and Classification of covering spaces.
Author(s): Alex Kuronya
102 Pages