We will use Hatcher's Algebraic Topology and will supplement a bit from his other two books (here and here ).
Syllabus
We will cover higher homotopy groups, homology and cohomology, and additional topics (e.g., stable homotopy groups of spheres, spectral sequences, homological stability).
Miscellany
Minhyong Kim's IHES lectures on fundamental groups in arithmetic. The first 30min contain a great discussion on "fiber functors" and gives another great perspective on pi_1.