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The Book - Basics of The Finite p-Groups has been designed purposely for students (graduates and intermediates) in the field of Algebra of general group theory and most especially, the aspect of finite p-groups. It gives foundations and linkage to research students whose major interests lie in the concepts of analysis of p-groups and groups in general. The aim is to bridge the gaps of deficiency in the foundation and general concept of Groups of prime power order, otherwise referred to as the finite p-groups. We have made the book fully simplified. This makes it very useful most especially to graduate students and researchers in their introductory stages. Clearly, the basic terms which are indispensable in this rich and dynamic field of mathematics have been discussed. It is also glaring how application is made into other branches of mathematics and generally into the field of real life. Our hope and expectation to the readers and users is that reading this book will certainly catapult and launch you into greater, enviable and attainable heights in finite p-groups and general pure and applied mathematics.