The homology of iterated loop spaces

The chain complex of the iterated loop space is expressed through the chain complex over an initial space in terms of the cobar construction. The corresponding spectral sequence is constructed and its first term is calculated. Applications to the calculation of the homology of the iterated loop spaces of the stunted real and complex projective spaces are given. The origin of this work is in some machine computations undertaken by Sergeraert; a brief report about them is given in the appendix.