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This book is prepared for the initial acquaintance with Manifold theory. Today's model of space, on which most of the new work in geometry and theoretical physics is done. It is clear that in the first lesson it is not possible to discuss all the topics of a theory in detail. After introducing the Manifold concept, it is necessary to introduce a structure on it. Most structures on manifolds are made of tensor fields. Based on this, simpler concepts such as tangential space, vector field, differential form and tensor field are introduced.