Prison Notebooks is a rather fragmentary collection of notes that Antonio Gramsci wrote while the Mussolini regime locked him up in an Italian prison for 20 years. Gramsci would never see freedom again - he died in prison in 1937 - and was isolated most of the time (both in terms of visits by people as in terms of information access). Still, he was able to write hundreds and hundreds of pages of critique, commentary, etc. relating to events taking place in the world prior to him ending up in jail and on general (marxist) theories.
The problem with Gramsci is that many of his notes contradict earlier notes and many of his ideas are vague, open-ended and obscure (on purpose: to cicrumvent the fascist prison censorship). This makes it very hard to spot clear and distinct ideas. Nevertheless, this approach also allows for insightful comparative analyses and viewing Gramsci's ideas from various perspectives (e.g. one could argue that the modern 'right wing' has learned a thing or two from Gramsci).
Still, it is possible to distill a certain theoretical approach which characterizes Gramsci's thoughts on politics, history and culture.
The first important concept in Prison Notebooks is the infamous base-superstructure distinction of society. Society is founded in social relations (i.e. relations determined by economic production) in reality. Built on top of this foundation are society's superstructures: its institutions that originate in and promulgate the particular social relationships. So, a capitalist system of production will produce capitalist superstructures which in one sense resemble the system and in another sense help to keep the system functioning effectively. For example, institutions which regulate sexual behaviour (marriage) or those which sustain productive labour (trade unions) are all part of the superstructure. (This by the way also explains Gramsci's rejection of trade unions as solutions to the capitalistic contradictations.)
Another concept of Gramsci's - and one related to the above mentioned distinction - is the triad of civil society, the State and 'war of position'. Civil society is the mediator between the State and economic production. This relation is very important since Gramsci distinguishes the term 'hegemony' from 'authority'. The State in and of itself is nothing but the power of coercion and in this form will never be able sustain the current structure of economic production: it needs moral and ideological leadership and those can only come from intellectuals within society and the public sphere.
In setting up his theories in this way, Gramsci is able to overcome a fundamental problem of Marxism: the problem of acquiring power to overthrow the current system and build a new one (i.e. revolution). Gramsci recognizes the problem of this 'frontal attack' approach - any violent coup or revolution (as well as any reform, by the way) plays itself out *within* the current system and thus will be absorbed *by* the system. The end result will most times be utter failure to accomplish any preconceived set of goals, and at most it will cancel a few contradictions and create new ones in its turn. In other words: a violent attack on the State and the subsequent grab of State power mostly won't change anything and if it does change a thing, it'll be local and temporary as it creates new problems in its wake.
For Gramsci, the succes of a Communist Party in building a totalitarian society according to communist goals depends on first acquiring hegemony within civil society and only after this to grabbing State power. This means organizing and uniting classes; growing organic intellectuals representing their classes; and having these occupy 'enemy positions' (hence the 'war of position' term). Only by taking over most of the enemy's positions can an effective coup be launched to grab State power to build a totalitarian society modelled on communist theories. So, where Marxist and Marxist-Leninists organized class power to attack the State, Gramsci wants Marxists to infiltrate the civil institutions, win over the masses through moral and ideological leadership, and in so doing to 'organically' accumulate social force to overthrow the State. In other words: the ground has to be seeded first in order to reap the rewards later on - the infamous 'long march through the institutions'.
Connected to the ideas set out above is Gramsci's conception of philosophy: to him all thinking is grounded in reality and done by all human beings. This means that in effect all human beings are intellectuals. His conception of philosophy (critique, i,e, viewing the objects of knowledge as fundamentally connected with the process of acquiring knowledge, cf. Hegel) is rooted in praxis: the actual lives and actions of people of flesh and blood; instead of the usual abstractions many philosophers use. This results in Gramsci's view that all philosophy (or rather: all thinking) is political.
Since all thinking is political, and politics is rooted in the real world, this means that all philosophy (i.e. all critical thinking) should be firmly rooted in its social-historical context. In claiming this, Gramsci sticks to Marx's historicism while at the same time giving it his own twist, offering room for idealism as well as strategic-practical approaches.
The above outlines sum up Gramsci's core ideas and central theses. In Prison Notebooks he uses hundreds and hundreds of pages to work out his ideas, offering detailed historical analyses of, for example, the 19th century Risorgimento and the rise of Fascism in the 1920s. This makes the book a very interesting historial time capsule while at the same time offering modern readers highly biased and outdated material... It depends mostly on one's reading angle whether the former or latter conclusion holds.
Perfectly in line with Gramsci's dialectics I found this book to have continuous contradictions and pros and cons. Certain passages I skipped, while others were truly interesting. Let's leave it at three stars for an interesting and very influential work. I think one can get a representative and comprehensive account of Gramsci's core theories and ideas without having to plough through 400+ pages of the Prison Notebooks (which, by the way, was a small selection of all his notebooks he wrote while in prision).