The book is a short introduction to the theory of knowledge, organized as a sequence of problems rather than a system. Russell begins with a deceptively simple question: is there any knowledge so certain that no reasonable person could doubt it? To test it he examines an ordinary table and shows that its colour, shape, and hardness vary with the observer, so that what we directly perceive is not the table itself.
He introduces the term sense-data for the colours, sounds, and textures we are immediately aware of, distinct from the sensation of being aware of them. The real table, if it exists, is a physical object inferred as the cause of these sense-data. This opens the questions that occupy the early chapters: whether matter exists at all, and what its nature could be, with Berkeley's idealism examined and set against the instinctive belief in an independent world.
A central distinction follows: knowledge by acquaintance and knowledge by description. We are acquainted with sense-data, with memories, with our own inner states, and with universals, but our knowledge of physical objects and of other people is by description, built from truths that connect them to things we do know directly. All knowledge, Russell argues, rests ultimately on acquaintance.
He then turns to the general principles that let us reason beyond present experience. Induction, the belief that uniform past sequences will continue, cannot be justified by experience without circularity, yet without it science and even daily expectation collapse. Russell also defends a priori knowledge, drawing on Kant and Hume, and revives a broadly Platonic account of universals as real but non-physical entities apprehended by thought. Later chapters treat truth as correspondence, the difference between knowledge, error, and probable opinion, and the limits of what metaphysics can establish.
The closing chapter steps back to ask why philosophy is worth studying. Russell concedes it yields few settled results, but argues this is its strength. By keeping alive questions that science cannot answer, philosophy frees the mind from the tyranny of custom, enlarges the self through contemplation of what is not the self, and turns a person from a prisoner of private interest into a citizen of the universe.