This article extends the Berry-phase formulation of electric polarization in crystals to higher electric multipole moments, specifically quadrupole and octupole moments. The authors determine the conditions under which these moments are topologically quantized electromagnetic observables in crystalline systems. They introduce a new paradigm using nested Wilson loops to characterize these topological invariants, which have been previously overlooked. The quantization of these moments is protected by crystalline symmetries, leading to gapped boundaries with lower-dimensional topological phases and corner states carrying fractional charges. The authors propose three experimental implementations of these topological phases in cold-atom lattice systems and photonic crystals, which can be tested immediately. The article provides a detailed theoretical framework and numerical simulations to support these findings.This article extends the Berry-phase formulation of electric polarization in crystals to higher electric multipole moments, specifically quadrupole and octupole moments. The authors determine the conditions under which these moments are topologically quantized electromagnetic observables in crystalline systems. They introduce a new paradigm using nested Wilson loops to characterize these topological invariants, which have been previously overlooked. The quantization of these moments is protected by crystalline symmetries, leading to gapped boundaries with lower-dimensional topological phases and corner states carrying fractional charges. The authors propose three experimental implementations of these topological phases in cold-atom lattice systems and photonic crystals, which can be tested immediately. The article provides a detailed theoretical framework and numerical simulations to support these findings.