This paper presents a novel structured knowledge representation called the functional object-oriented network (FOON) to model the connectivity of the functional-related objects and their motions in manipulation tasks. The graphical model FOON is learned by observing object state change and human manipulations with the objects. Using a well-trained FOON, robots can decipher a task goal, seek the correct objects at the desired states on which to operate, and generate a sequence of proper manipulation motions. The paper describes FOON's structure and an approach to form a universal FOON with extracted knowledge from online instructional videos. A graph retrieval approach is presented to generate manipulation motion sequences from the FOON to achieve a desired goal, demonstrating the flexibility of FOON in creating a novel and adaptive means of solving a problem using knowledge gathered from multiple sources. The results are demonstrated in a simulated environment to illustrate the motion sequences generated from the FOON to carry out the desired tasks.