Self-Sovereign Identity (SSI) is a novel and emerging, decentralized digital identity approach that enables entities to control and manage their digital identifiers and associated identity data fully while enhancing trust, privacy, security, and the many other properties identified and analyzed in this paper. The paper provides an overview and classification of the SSI properties, focusing on an in-depth analysis, furthermore, presenting a comprehensive collection of SSI properties that are important for the implementation of the SSI system. In addition, it explores the general SSI process flow, and highlights the steps in which individual properties are important. After the initial purification and classification phase, we then validated properties among experts in the field of Decentralized and Self-Sovereign Identity Management using an online questionnaire, which resulted in a final set of classified and verified SSI properties. The results can be used for further work on definition and standardization of the SSI field.