This course is designed to provide the students with some of the necessary potential research  background from the homological algebra for reading and understanding research articles in algebraic topology. In particular, it is designed to equip the students with the essential computational technique of spectral sequences and Steenrod algebra, to give applications to spaces with a group action, to introduce some topics of algebraic topology such as group cohomology and transformation groups, which are  potential research areas for graduate  students.