This graduate textbook introduces the analysis of fractals, particularly dynamical aspects such as heat diffusion on fractals and the vibration of a material with fractal structure. Kigami (Kyoto University) explains how to construct Dirichlet forms, harmonic functions, Green's functions and Laplacians on post critically finite self-similar sets, and examines eigenvalues and eigenfunctions of Laplacians and heat kernels associated with Laplacians.