The lens design is a fundamental but challenging problem, while modern lens design processes still follow the classic aberration optimization theory and need preliminary designs and experienced optical engineers to control the optimization process constantly. In this thesis, we develop a differentiable ray-tracing model and apply it to automatic lens design. Our method can do ray-tracing and render images with high accuracy, with the power to use the back-propagated gradient to optimize optical parameters. Different from traditional optical design, we propose to use the rendered images as the training criteria. The rendering loss shows superior results in optimizing lenses while also making the task easier. To remove the requirements of preliminary design and constant operations in conventional lens design, we propose a curriculum learning method that starts from a small aperture and field-of-view(FoV), gradually increases the design difficulty, and dynamically adjusts attention regions of rendered images. The proposed curriculum strategies empower us to optimize complex lenses from flat surfaces automatically. Given an existing lens design and setting all surfaces flat, our method can entirely recover the original design. Even with only design targets, our method can automatically generate starting points with flat surfaces and optimize to get a design with superior optical performance. The proposed method is applied to both spheric and aspheric lenses, both camera and cellphone lenses, showing a robust ability to optimize different types of lenses. In addition, we overcome the memory problem in differentiable rendering by splitting the differentiable rendering model into two sub-processes, which allows us to work with megapixel sensors and downstream imaging processing algorithms.