1. Establish a solid mathematical foundation: differential geometry involves many advanced mathematical knowledge, such as calculus, linear algebra and group theory. So, first of all, we need to have a deep understanding and mastery of these basic knowledge.
2. Understand the basic concepts of differential geometry: There are many abstract concepts in differential geometry, such as manifold, tangent, normal and curvature. Understanding these concepts is the basis of learning differential geometry.
3. Learn the basic theory of differential geometry: the theoretical system of differential geometry is very huge, including Riemannian geometry, affine geometry, projective geometry and many other sub-fields. Each sub-field has its own unique theories and methods, which need to be studied and understood one by one.
4. Hands-on practice: While theoretical study is important, it is more important to consolidate and apply what you have learned by doing exercises. The exercises of differential geometry often need to use a variety of methods and skills, which is very helpful to improve the ability to solve problems.
5. Read professional books and papers: In addition to teaching materials, you can also read some professional differential geometry books and papers to gain more in-depth and extensive knowledge.
6. Participate in academic discussions and research: If you have the opportunity, you can participate in some academic discussions and research activities, exchange learning experiences with classmates and teachers, and discuss problems together, which is very helpful to improve the learning effect.
Generally speaking, it takes time and energy to learn differential geometry well, but as long as you have enough enthusiasm and perseverance, you will certainly get satisfactory results.