The Tractatus is a short, severe book built as a tree of numbered statements rather than as continuous argument. Seven main propositions carry the weight, and the decimal numbers beneath them (1.1, 1.11, and so on) are comments that expand or qualify the point above. There are no chapters and almost no transitions. The reader is asked to follow a single chain of thought from the structure of the world down to the limits of language and out to what must be left unsaid. C. K. Ogden's translation prints the German and English side by side, and Bertrand Russell's Introduction lays out the route in advance: from the logic of propositions to knowledge, physics, ethics, and finally the mystical.
It opens with the world. The world is everything that is the case, and it is a totality of facts, not of things. Facts are made of atomic facts, which are combinations of objects, and objects are the fixed substance that every possible situation is built from. Reality is then the existence and non-existence of these atomic facts. This is not a survey of what happens to exist but a claim about the form any world must have if it can be described at all.
From the world the book turns to thought and language through its picture theory. We make pictures of facts, and a logical picture shares a form with what it depicts: its elements are arranged as the things in the situation are arranged. A proposition is just such a picture put into words. Because it shares logical form with reality, it can be laid against the world and found to agree or not, which is what makes it true or false. A name stands for an object only inside a proposition, and only the whole proposition has a sense. The thought is the proposition with a sense.
The middle of the book works out logic. Ordinary propositions are truth-functions of simpler elementary propositions, and complex sense is built up from these by combination. The propositions of logic are tautologies: they say nothing about the world but display the formal scaffolding shared by all language. This lets Wittgenstein turn on philosophy itself. Most philosophical propositions and questions, he says, are not false but senseless, the result of failing to understand the logic of our language. So philosophy is not a doctrine but an activity of clarification, marking the boundary between what can be said clearly and what cannot be said at all.
The closing propositions press to the edge of that boundary and then over it. The limits of language mean the limits of one's world; solipsism, carried out strictly, collapses into pure realism, and the thinking subject turns out to be a limit of the world rather than a part of it. Since everything in the world simply is as it is, value cannot lie within it: ethics and aesthetics cannot be stated, only shown. What is higher, the sense of life, the world felt as a limited whole, is the inexpressible, the mystical. Wittgenstein then admits that his own sentences are elucidatory only, a ladder to be thrown away once it has been climbed. The book ends with its seventh proposition: whereof one cannot speak, thereof one must be silent.