Poly(propylene fumarate) (PPF) is an important biodegradable and cross-linkable polymer designed for bone-tissue-engineering applications. For the first time we report the extensive characterization of this biomaterial including molecular weight dependences of physical properties such as glass transition temperature T-g, thermal degradation temperature T-d, density rho, melt viscosity eta(0), hydrodynamic radius R-H, and intrinsic viscosity [eta]. The temperature dependence of eta(0) changes progressively with molecular weight, whereas it can be unified when the temperature is normalized to T-g. The plateau modulus G(N)(0) and entanglement molecular weight M-e have been obtained from the rheological master curves. A variety of chain microstructure parameters such as the Mark-Houwink-Sakurada constants K and alpha, characteristic ratio C-infinity, unperturbed chain dimension r(0)(2)/ M, packing length p, Kuhn length b, and tube diameter a have been deduced. Further correlation between the microstructure and macroscopic physical properties has been discussed in light of recent progress in polymer dynamics to supply a better understanding about this unsaturated polyester to advance its biomedical uses. The molecular weight dependence of T-g for six polymer species including PPF has been summarized to support that M-e is irrelevant for the finite length effect on the glass transition, whereas surprisingly these polymers can be divided into two groups when their normalized T-g is plotted simply against M-w to indicate the deciding roles of inherent chain properties such as chain fragility, intermolecular cooperativity, and chain end mobility.