  We prove convergence of renormalized correlations of primary fields, i. e.,
spins, disorders, fermions and energy densities, in the scaling limit of the
critical Ising model in arbitrary finitely connected domains, with fixed (plus
or minus) or free boundary conditions, or mixture thereof. We describe the
limits of correlations in terms of solutions of Riemann boundary value
problems, and prove their conformal covariance. Moreover, we prove fusion
rules, or operator product expansions, which describe asymptotics of the
scaling limits of the correlations as some of the points collide together. We
give explicit formulae for correlations in the case of simply-connected and
doubly-connected domains. Our presentation is self-contained, and the proofs
are simplified as compared to the previous work where particular cases are
treated.
