Recently found a wonderful topology notes, suitable for beginners at: http://mathcircle.berkeley.edu/archivedocs/2010_2011/lectures/1011lecturespdf/bmc_topology_manifolds.pdf
It starts by pondering the shape of the earth, then generalizes to other surfaces. It also has a nice section on Fundamental Polygons and cutting and gluing, which was what I was looking for at first.
I have backed up a copy on Mathtuition88.com, in case the original site goes down in the future: bmc_topology_manifolds
Mathtuition88 
These notes should be called “Topology with smiles” !! 🙂 🙂 🙂 It takes a lot to simplify a subject like Topology and explain to a beginner !!
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Yes indeed! One of the best beginner topology notes that I have seen in the past few years.
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