Endmember extraction is a fundamental data processing for many applications in hyperspectral data exploitation such as anomaly detection, spectral unmixing, classification, data compression, image analysis etc. Since an endmember is defined as a pure, idealized signature for a spectral class, it provides first hand information for image understanding and analysis. Many algorithms have been designed and developed for endmember extraction in the past. One of popular criteria, maximim simplex volume (MSV), have been used for this purpose, which results in a popular algorithm, MSV-based N-finder algorithm (N-FINDR). The research proposed in this proposal is primarily focused on design and analysis of Endmember Extraction Algorithms (EEAs). In particular, four major contributions are made in this proposal. One is new algorithms, referred to as Simplex Growing Algorithm (SGA) that improves the N-FINDR in many aspects. The second contribution is to develop a new sequential version of commonly used N-FINDR, referred to as SuCcessive N-FINDR (SC N-FINDR). The third and fourth contributions are to design and develop initialization-driven and random versions of EEAs to address issues caused by the use of random initial endmembers implemented in EEAs.