The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gâteaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key elem...