This paper extends the chiral perturbation theory framework to expansions in the mass of the strange quark. The authors construct the generating functional of U(3)×U(3) to calculate all Green's functions up to and including terms of order \( p^4 \) (at fixed ratio \( m_s/p^2 \)) in terms of a few coupling constants that chiral symmetry leaves undetermined. They calculate the first non-leading term in the quark mass expansion of order parameters and masses and decay constants in the pseudoscalar octet. The three coupling constants not fixed by experimental low-energy information are estimated using large \( N_c \) arguments. The paper covers the construction of the generating functional, the effective low-energy Lagrangian, the ground state, and the low-energy expansion at leading order. It also discusses the effective Lagrangian to order \( p^4 \) and the one-loop graphs. The results provide a systematic way to determine the low-energy structure of Green's functions in QCD, particularly in the context of SU(3) flavor symmetry and the validity of chiral symmetry.This paper extends the chiral perturbation theory framework to expansions in the mass of the strange quark. The authors construct the generating functional of U(3)×U(3) to calculate all Green's functions up to and including terms of order \( p^4 \) (at fixed ratio \( m_s/p^2 \)) in terms of a few coupling constants that chiral symmetry leaves undetermined. They calculate the first non-leading term in the quark mass expansion of order parameters and masses and decay constants in the pseudoscalar octet. The three coupling constants not fixed by experimental low-energy information are estimated using large \( N_c \) arguments. The paper covers the construction of the generating functional, the effective low-energy Lagrangian, the ground state, and the low-energy expansion at leading order. It also discusses the effective Lagrangian to order \( p^4 \) and the one-loop graphs. The results provide a systematic way to determine the low-energy structure of Green's functions in QCD, particularly in the context of SU(3) flavor symmetry and the validity of chiral symmetry.