Disclaimer: I've literally hoisted these dinosaurs out of the archives.

Make of this what you will. The preceding warning remains in effect.

That being said, I've just finished touching these files up quite a bit. These notes come from a variety of sources but principally from Munkres' topology textbook. The files are in the order that they ought to be read in.

Rudimentary Elements of Topology
Quotients and Adjunctions
Notions of Connectedness
Compact and LCH Spaces
Regular and Normal Spaces
Urysohn's Lemma and The Tietze Extension Theorem
Urysohn's Metrization Theorem and the Emebedding Theorem
The Stone-C̆ech Compactification
Locally Finite Collections and the Nagata-Smirnov Metrization Theorem
Paracompact Spaces and the Smirnov Metrization Theorem
Topologies on Function Spaces and Ascoli's Theorem