This is a note that describes how a Convolutional Neural Network (CNN) operates from a mathematical perspective. This note is self-contained, and the focus is to make it comprehensible to beginners in the CNN eld. The Convolutional Neural Network (CNN) has shown excellent performance in many computer vision and machine learning problems. Many solid papers have been published on this topic, and quite some high quality open source CNN software packages have been made available. There are also well-written CNN tutorials or CNN software manuals. However, I believe that an introductory CNN material speci cally prepared for beginners is still needed. Research papers are usually very terse and lack details. It might be difficult for beginners to read such papers. A tutorial targeting experienced researchers may not cover all the necessary details to understand how a CNN runs. Introduction to Convolutional Neural Networks