The photoproduction of 2$pi^0$ mesons off protons was studied with the Crystal Barrel/TAPS experiment at the electron accelerator ELSA in Bonn. The energy of photons produced in a radiator was tagged in the energy range from 600,MeV to 2.5,GeV. Differential and total cross sections and $ppi^0pi^0$ Dalitz plots are presented. Part of the data was taken with a diamond radiator producing linearly polarized photons, and beam asymmetries were derived. Properties of nucleon and $Delta$ resonances contributing to the $ppi^0pi^0$ final state were determined within the BnGa partial wave analysis. The data presented here allow us to determine branching ratios of nucleon and $Delta$ resonances for their decays into $ppi^0pi^0$ via several intermediate states. Most prominent are decays proceeding via $Delta(1232)pi$, $N(1440)1/2^+pi$, $N(1520)3/2^-pi$, $N(1680)5/2^+pi$, but also $pf_0(500)$, $pf_0(980)$, and $pf_2(1270)$ contribute to the reaction.
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