In this part, we derive the complete and irreducible representations for two dimensionalorthotropic functions and two and three dimensional relative isotropic (i.e. the symmetry group is theproper orthogonal tensor group) functions of symmetric tensors, skew-symmetric tensors and vectors. The functions may be any general (not only polynomial) scalar-valued, vector-valued, symmetrictensor-valued and skew-symmetric tensor-valued ones. The complete representations for threedimensional transversely isotropic and orthotropic functions are derived in Parts II and IVrespectively and their irreducibility is proved in Parts III and V respectively.