This thesis introduces a research project completed by Yueheng Peng. All the study are based on numerical simulation method. The first part described about the history of negative refractive index material, including difference with conventional materials and recent advances in metamaterials research and discuss the potential that these materials may hold for realizing new phenomena and application. Secondly, our own deep understanding and theory of metalens is proposed and explained clearly. The third part illustrated how to design 2-D & 3-D metalens and simulation results, at different numerical aperture, we can achieve efficiency more than 60%. Then we will talk about the optical characterization. With the help of camera (DCC3240C, Thorlabs), we can observe the characterized field distribution on the plane of focus. The last two parts are about Linear Distinguishing Metalens and Metalens providing focus in different shapes. In this study, we propose a metalens that integrates the function of concentrating lens and linear polarizer. All the results are based on Finite Difference Time Domain (FDTD) simulation method in electromagnetism. The entire thesis is structured as following: 1. Introduction and Basic Theory of Metalens; 2. Deep understanding and multiple theories of metalens. 3. 2-D & 3-D lens: Design and Optical Characterization; 4. Linear Distinguishing Metalens; 5. 3-D Metalens with Focus in Different Shapes.