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Adaptive algorithm is the algorithm that can change its behavior as it desired by the user. The analysis of the algorithm may be worst case analysis measured by the performance that may lead towards average case and best case analysis. In this book I have made the objective that the performance analysis of different adaptive algorithms can be evaluated for the application of system identification and noise cancellation. Among many applications of adaptive filters on common application is to identify an unknown system, it means the response of an unknown channel or frequency response can be determined and the error can be evaluated for minimization through different algorithms like LMS, NLMS and different variants of LMS algorithm. We have introduced different norms based on LMS algorithm to overcome slow convergence of standard LMS algorithm in the application of system identification. Similar to the application of system identification we have considered another application as noise cancellation. The objective is to study the adaptive filter theory for noise cancellation problem.