Lectures on differential geometry

Preface: These are lectures on differential geometry written for undergraduate students at University College Cork in 2017. They assume elementary knowledge of metric spaces and topological spaces, including the concepts of homeomorphism, Hausdorff space, quotient space, and covering space. I recommend the reader on a first reading skip any section that says it can be omitted, and skip all problems marked with a ˚, although it might be worthwhile to read the hints to the ˚ problems.