Endmember extraction is a fundamental task and has been found in 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 major criteria, maximum simplex volume ( MSV) has been used for this purpose. One best well- known Endmember Extraction Algorithm ( EEA) in this category is N- finder algorithm ( N- FINDR) developed by Winter. However there are many issues arising in its practical implementation. The research proposed in this dissertation is to investigate and resolve these issues. As a result, N-FINDR has been either re- invented to derive new algorithms such as Simplex Growing Algorithm ( SGA) and Random N- FINDR ( RN- FINDR) or re- designed to better suit practical implementation such as SeQuential N- FINDR ( SQ N- FINDR), SuCcessive N-FINDR ( SC N- FINDR), Initialization- Driven N- FINDR ( ID N- FINDR) and Causal N-FINDR. In order to substantiate all the algorithms proposed in this dissertation, synthetic image- based experiments are conducted for validation. To further demonstrate their utility in real applications two real hyperspectral image data sets are also performed for experiments. Finally, a comparative analysis between N- FINDR and other popular EEAs is also studied to explore their relationships.