Algebraic Topology pamphlets?

http://tartarus.org/gareth/maths/notes/ has the notes from our year.

http://www.math.tifr.res.in/~publ/pamphlets/algtop.pdf

http://www.math.tifr.res.in/~publ/ln/tifr44.pdf

My book Topology and Groupoids is one of few at this level to give an account of the van Kampen theorem with lots of applications (cell complexes, knots, Jordan Curve Theorem) and of covering spaces, both in terms of fundamental groupoids. (You also get orbit spaces, which you won't find elsewhere in English.) A pdf is available through the above web page.

A proof of a general version of the van Kampen theorem for the fundamental groupoid on a set of base points and a union of many open sets is available here (the proof is no harder than doing it for one base point!)

The pushout version for a union of two sets with two base points allows the computation of the fundamental group of the circle, which is, after all, THE basic example in algebraic topology. For that example, one base point is not enough, but two will do.

See also this mathoverflow link for more discussion on several base points; this image

shows a union of 3 spaces which requires $8$ base points to encapsulate the symmetry information.