In this chapter we have collected some further notions about categories, preadditive categories, additive categories and abelian categories. Thus we present monomorphisms in arbitrary categories, epimorphisms, subobjects, quotient objects, products and coproducts of objects, biproducts in a preadditive category, initial objects, null objects, terminal objects, zero morphisms, additive functors between preadditive categories, equalizers, coequalizers, kernels and cokernels, with several examples. We give an example of two preadditive categories that are isomorphic as categories, but are not isomorphic as preadditive categories.