We present the first measurement of decay amplitudes in B-->phiK(*) and measurements of branching fractions in B-->phiK((*)) decays based on 78.1 fb(-1) of data recorded at the Y(4S) resonance with the Belle detector at the KEKB e(+)e(-) storage ring. The decay amplitudes for the different phiK(*0) helicity states are measured from the angular distributions of final state particles in the transversity basis. The longitudinal and transverse complex amplitudes are \A(0)\(2)=0.43+/-0.09+/-0.04, \A(perpendicular to)\(2)=0.41+/-0.10+/-0.04, arg(A(parallel to))=-2.57+/-0.39+/-0.09, and arg(A(perpendicular to))=0.48+/-0.32+/-0.06. The direct CP-violating asymmetries are found to be consistent with zero.