General methods for evaluating three-electron integrals in Hylleraas coordinates are given. Formulae are obtained for the matrix elements of various operators arising in Hylleraas-type variational calculations for states of arbitrary angular momentum. For the calculations of Breit interaction, a number of reduction relations are developed for the elimination of singularities in some singular integrals. A numerically stable scheme is presented for the case when one of the powers of is -2.