Contradiction - A proposition that is false no matter what is the case or is not the case. A contradiction lacks sense, but is not nonsensical.
Fact - A complex made up of states of affairs. The world is the totality of "positive facts," i.e. facts that are the case.
Logical space - The space in which objects and states of affairs exist. This is the most general kind of space there is, so everything that exists and everything that could exist exists in logical space.
Object - The simple items that constitute states of affairs. Objects can only exist within the context of states of affairs. They have a internal properties—their logical form—and external properties—whatever properties are ascribed to them in states of affairs.
Operation - The process by which one proposition is generated out of another. Operations are not themselves "things" in any sense of the word: they are simply the expression of a commonality (a common logical form) that exists between two propositions. All propositions can be generated by means of a single negating operation applied successively to elementary propositions.
Proposition - The means of transmitting thoughts. A proposition can take the form of written, spoken, or any other kind of communication. It is made up of simple names arranged in a particular logical form. A proposition thus serves as a picture of the facts it represents. Most propositions are complex; simple propositions are called "elementary propositions."
Solipsism - The philosophical position that nothing exists but outside of oneself. My world consists only of sensory stimuli, and so I cannot rightly say there are people or things in the world around me, only my own impressions of people and things. This is obviously a difficult position to maintain (why do I bother expressing this position if I don't believe there are other people out there who will consider it?), but it also notoriously difficult to disprove.
State of affairs - The simplest form of facts. States of affairs are utterly simple, unanalyzable, and mutually independent. The totality of states of affairs is the world.
Tautology - A proposition that is true regardless of what is and what is not the case. As such, tautologies lack sense (but are not nonsense) and say nothing. Wittgenstein asserts that the propositions of logic are tautologies, thus underscoring the idea that the propositions of logic can say anything about the world.
Thought - By "thought," Wittgenstein does not refer to a psychological entity, but to a logical one. We are able to think about facts and propositions because our thoughts share a logical form with facts and propositions. Thus, we are able to put our thoughts into the world in the form of propositions.
World - "The world is all that is the case." Wittgenstein generally uses "world" to refer to the totality of all facts. If we were to make an itemized list of every true proposition, this itemized list would be a full description of the world. Sometimes, however, Wittgenstein uses "world" to refer to the totality of both positive and negative facts, both to what is and what is not the case. He is referring then to everything that is logically possible.