Ramian Engineering translation Dr. Nasser Ibrahim Al-Turki

This book presents the main concepts in Riemannian geometry. And in order to overcome the difficulty of understanding the complex formulas of Riemannian geometry, the book begins with curvature, which is one of the most important concepts in differential geometry, and also the book at its beginning studies curves and surfaces with two-dimensional extent. Curvature in geometry is known as the measure of deviation in the geometric shape. Then the book expands to study surfaces with three-dimensional extent. It also provides an introduction to Riemannian geometry starting from the Riemannian manifold. After that, more complex topics are studied, including hyperbolic geometry, projective geometry, and some theorems in Riemannian geometry.