The Infrared Atmospheric Sounding Interferometer (IASI) is a hyperspectral sensor with 8461 spectral channels and a nominal spectral resolution of 0.25 cm(sup -1). It is computationally intensive to perform radiative transfer calculations and inversions using all these channels. We will present a Principal Component-based Radiative Transfer Model (PCRTM) and a retrieval algorithm which perform all the necessary calculations in EOF domain. Since the EOFs are orthogonal to each other, only about 100 principal components are needed to represent the information content of the 8461 channels. The PCRTM provides the EOF coefficients and associated derivatives with respect to atmospheric and surface parameters needed by the inversion algorithm. The inversion algorithm is based on a non-linear Levenberg-Marquardt method with climatology covariance and a priori information as constraints. The retrieved parameters include atmospheric temperature, moisture and ozone profiles, cloud parameters, surface skin temperature, and surface emissivities. To make the retrieval system even more compact and stable. The atmospheric vertical profiles are compressed into the EOF space as well. The surface emissivities are also compressed into EOF space.