This book mainly deals with the Bochner-Riesz means of multiple Fourier integral and series on Euclidean spaces. It aims to give a systematical introduction to the fundamental theories of the Bochner-Riesz means and important achievements attained in the last 50 years. For the Bochner-Riesz means of multiple Fourier integral, it includes the Fefferman theorem which negates the Disc multiplier conjecture, the famous Carleson-Sjoelin theorem, and Carbery-Rubio de Francia-Vega's work on almost everywhere convergence of the Bochner-Riesz means below the critical index. For the Bochner-Riesz means of multiple Fourier series, it includes the theory and application of a class of function space generated by blocks, which is closely related to almost everywhere convergence of the Bochner-Riesz means. In addition, the book also introduce some research results on approximation of functions by the Bochner-Riesz means.