Band selection (BS) is an effective means to solve the problems of spectral redundancy and Hughes phenomenon in hyperspectral images (HSIs). However, existing BS methods fail to consider the representativeness, redundancy, and information content of the selected bands simultaneously, and most of them lack consideration of the inherent nonlinear relationship between bands. To address these problems, we propose a novel unsupervised BS framework that can comprehensively consider band representativeness, redundancy, and information content (RRI) in this letter. The band representativeness is estimated by a convolutional autoencoder (AE), which can capture the inherent nonlinear relationship between the bands and leverage the spatial information of the HSI. The redundancy and the information content of a band subset are restricted and enhanced by the correlation coefficient and the information divergence (ID), respectively. Subsequently, RRI combines these three indicators as the subset evaluation criterion and utilizes an immune clone selection algorithm to search for the desired band subset. Experimental results verify that the proposed RRI method can provide higher classification accuracy than the competitors and is robust to noisy bands.