Ludwig Wittgenstein contributed two major pieces of work to philosophy. The first, the Tractatus, was a celebrated attempt to systematically explain language as a form of representation which, to be meaningful, has to represent the world in terms that can be confirmed by experience. In this way, he hoped to finally solve all philosophical problems by eliminating them as meaningless. Metaphysics, for instance, which does not make statements verifiable by experience, is therefore meaningless and so no longer a problem. Having written it, Wittgenstein gave up philosophy altogether for some time.
The second work, Philosophical Investigations, was written later, after doubts led him to return to Cambridge and take up philosophy again. Following 10 years of working through his ideas with students and fellows in lectures, he was elected to the chair of philosophy. The Investigations being the condensate of these discussions, sets about refuting his previous work and similar approaches, replacing them with a non-systematic, non-representational view of language. Nevertheless his aim of eliminating many philosophical conundrums remained, although in contrast to his previous work, many are now only transformed into new, more practical, forms.
In the introduction to the Investigations Wittgenstein writes:
I should not like my writing to spare other people the trouble of thinking. But, if possible, to stimulate someone to thoughts of his own.
Philosophical Investigations, Preface p viii
In this he was certainly successful. The work was unfinished, published after his death by his students. Possibly, by nature, it could never have been finished. It is a unique book in philosophy: if there are arguments, they are only implied. It is, instead, merely a series of "remarks" (Preface vii) intended to lead the reader through the landscape of our language, noting various features and comparing them with philosophical attempts to systematically describe them, including his own Tractatus,. It is perhaps his aim to show how the reality of language escapes them all. It is also perhaps his aim to indicate that language will likely escape any complete, systematic, analysis.