This is a series of courses on selected important topics in algebraic topology, which aims to help the research of the graduate students and junior researchers in pure and applied algebraic topology. During this semester, our selected topics will concentrate on Leray-Serre spectral sequence and its relevant topics, consisting of Barratt-Gugenheim-Moore simplicial fibre bundles theory, simplicial approach to the Leray-Serre spectral sequence with its comparison with the classical approach in the textbooks, sampling computations of spectral sequences performed by participated students, the applications in computing homotopy groups, Witten’s twisted de Rham cohomology with its comparison with Brown’s twisted tensor products, Grigor’yan-Muranov-Yau’s delta-cohomology and Delta-twisted homology.