This is a partial theory of thinking, combining a number of classical and modern concepts from psychology, linguistics, and AI. Whenever one encounters a new situation (or makes a substantial change in one's viewpoint) he selects from memory a structure called a frame, a remembered framework to be adopted to fit reality by changing details as necessary. A frame is a data-structure for representing a stereotyped situation, like being in a certain kind of living room, or going to a child's birthday party. Attached to each frame are several kinds of information. Some of this information is about how to use the frame. Some is about what one can expect to happen next. Some is about what to do if these expectations are not confirmed. The "top levels" of a frame are fixed, and represent things that are always true about the supposed situation. The lower levels have many "alota" that must be filled by specific instances or data. Collections of related frames are linked together into frame-systems. The effects of important actions are mirrored by transformations between the frames of a system. These are used to make certain kinds of calculations economical, to represent changes of emphasis and attention and to account for effectiveness of "imagery". In Vision, the different frames of a system describe the scene from different viewpoints, and the transformations between one frame and another represent the effects of moving from place to place. Other kinds of frame-systems can represent actions, cause-effect relations, or changes in conceptual viewpoint. The paper applies the frame-system idea also to problems of linguistic understanding: memory, acquisition and retrieval of knowledge, and a variety of ways to reason by analogy and jump to conclusions based on partial similarity matching.