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This book is designed as a text for readers who are doing higher mathematics and want to understand the subject in concise manner. The topics dealt with include Polynomial rings, Vector space theory,Inner product space,Gram Schmidt orthogonalisation process,Field theory(Extension of fields,Perfect field,Finite field). This book attracts the reader who wishes to do self-study. Key-features 1. Inclusion of lots of observation with easy proofs. 2. Gives simplified treatment of difficult topics. 3. Easy to grasp any concept. 4. Field theory in geometrical view.