In this talk, we will focus on first and second eigenvalues of Laplacian with boundary conditions, including Dirichlet, Neumann, Robin and Steklov eigenvalues. Particularly, we will show that geodesic balls in non-positively curved space forms and non-compact rank-1 symmetric space maximize the second Robin eigenvalue among bounded domains of the same volume. This talk is based on some joint works with Xiaolong Li(Wichita State University) and Haotian Wu (The University of Sydney).