Signatures have emerged as a powerful tool in machine learning, particularly for efficiently capturing key geometric features of data. In this report, we introduce the foundational concepts of signatures, outlining their essential properties such as invariance under time reparametrization, time-reversibility, and others. We further explore various applications of signatures, highlighting their versatility and utility. Finally, we revise the signature uniqueness theorem, which underscores the theoretical significance of signatures in the context of rough path theory.
