these lecture notes present an introduction to contact manifolds from the perspective of riemannian geometry. they are based on the author's lectures at the university of strasbourg and the university of liverpool in 1974-75. the text covers classical examples of contact manifolds, including principal circle bundles and tangent sphere bundles. the author discusses the geometry of these structures, focusing on contact metric manifolds and sasakian manifolds. the contact form on a contact manifold defines a contact distribution, which is not integrable. the maximum dimension of an integral submanifold is half that of the contact distribution. chapter v explores sasakian space forms, including their φ-sectional curvature and examples. chapter vi proves the non-existence of flat contact metric structures in dimensions ≥ 5. chapter vii examines the tangent sphere bundle as a contact metric manifold. the text also includes a bibliography and index. the author thanks his colleagues for their support and Mrs. Glendora Milligan for her assistance in preparing the manuscript. the book is intended for mathematicians interested in riemannian geometry and contact manifolds. it provides a comprehensive overview of the subject, with a focus on recent developments and classical examples. the text is well-structured, with clear explanations and detailed examples. it is an essential resource for researchers and students in the field of differential geometry.these lecture notes present an introduction to contact manifolds from the perspective of riemannian geometry. they are based on the author's lectures at the university of strasbourg and the university of liverpool in 1974-75. the text covers classical examples of contact manifolds, including principal circle bundles and tangent sphere bundles. the author discusses the geometry of these structures, focusing on contact metric manifolds and sasakian manifolds. the contact form on a contact manifold defines a contact distribution, which is not integrable. the maximum dimension of an integral submanifold is half that of the contact distribution. chapter v explores sasakian space forms, including their φ-sectional curvature and examples. chapter vi proves the non-existence of flat contact metric structures in dimensions ≥ 5. chapter vii examines the tangent sphere bundle as a contact metric manifold. the text also includes a bibliography and index. the author thanks his colleagues for their support and Mrs. Glendora Milligan for her assistance in preparing the manuscript. the book is intended for mathematicians interested in riemannian geometry and contact manifolds. it provides a comprehensive overview of the subject, with a focus on recent developments and classical examples. the text is well-structured, with clear explanations and detailed examples. it is an essential resource for researchers and students in the field of differential geometry.