This paper proposes a self-supervised dataset distillation (DSD) technique to address the high costs associated with the massive datasets required for training large-scale deep learning models. Unlike conventional supervised dataset distillation, we present a method for compressing images and representations obtained through self-supervised learning into a distilled dataset. To achieve this, we propose a novel method for parameterizing images and representations using low-dimensional bases, a pre-determined augmentation technique to address data augmentation instability, and a lightweight network for compressing distillation pairs. Experiments on various datasets demonstrate the effectiveness of the proposed method, its generalization performance across various architectures, and its superior transfer learning performance.