There has been speculation from both Centre-left and Centre-right newspapers that Jeremy Corbyn is a "Far-left". Given this sentiment, I'm going to break down Corbyn's views on various topics and then give an actual far-left position on it, and to make it fair i'll include a Libertarian far-left and an "authoritarian" far-left position on it rather than a broad sweep position on it.
But first, Who is Jeremy Corbyn? or rather what is he Ideologically that to the media he is seen as someone on the far-left? Jeremy Corbyn is a Democratic Socialist, which in the realm of Political Philosophy doesn't really say much about his political position since Democratic Socialists exist both in the Centre-left and the far-left so from that alone, its almost impossible to say one way or another. Some Democratic Socialists do hold some Economically Liberal views, like the PDP-Laban Party in the Philippines under Rodrigo Duterte. Ideologically driven Democratic Socialists are not new to British Politics, they are especially not rare in the Labour Party, One of the longest serving Democratic Socialists in the houses of commons is Dennis Skinner, another being Paul Flynn, both of which have been in Parliament longer than Corbyn has. So what is the big hype around Jeremy Corbyn, What views does he hold and are they actually far-left Positions? Let's break this down:
Taxation and the Economy
Jeremy Corbyn is in favour of re-nationalising the Railways and energy companies, now to a Liberal or Conservative, this may be seen as Radical. But this is not a new thing, the Labour Party has almost always had this stance on Nationalisation. Nationalisation or "bringing utilities into public ownership" is not an inherently Left wing idea or practice, there are many Right wing countries that nationalise certain industries, Russia is a good example of that, Putin is by no means left wing, and he'd probably knock you out if you insinuated that to his face.
A Libertarian Far-left position wouldn't be Nationalisation, since to the Libertarian far-left that's not democratically controlled at all. So to say its "public" ownership is being a bit dishonest about the relationship the state actually has not to the Nationalised company but the public itself. The Libertarian Far-left would Collectivise the Railways and services, actually bringing the control of the companies to the workers, not just the state. Allowing the Workers to decide what subsidies they need in order for the company work well.
An Authoritarian Far-left position would be nationalisation, but with some democratic control in the way of worker's councils where the state and workers can decide what is best economically for the company. Most people on the Auth Far-left would also say that you shouldn't just stop at the Railways but Airports, Ferries and major factories should also be brought into the hands of the state (and by proxy workers).
Education
Jeremy Corbyn is in favour of abolishing tuition fee's in England as well as across all of the UK (essentially following in Scotland's footsteps). Abolishing tuition fee's is a Socially Democratic idea, Social Democracy is inherently liberal in its analysis and for the most part is a Centre-left position, you see free tuition across most Socially Democratic countries, most famously the Scandinavian countries like Finland.
A Libertarian Far-left Position on Education in line with what Corbyn believes would be not just to abolish tuition fee's but to Abolish Capitalism entirely, guarantee the needs of everyone in Society. As well as give the option to those who have succeeded in Further Education to teach the new classes for 6-months to a year allowing the teachers who taught them time off work for their families whilst still being able to get their basic needs met.
A Auth Far-left Position, staying in line with the Marxist-Leninist view of a Transitional state that for the most part would still have a market economy of some description or another. The view wouldn't just be to Abolish the Tuition fee's but allow student's to choose when they come into school, what days, for how long, etc. As well as financing Student's while they are at college and university so that they can put 100% of their time into Studying. The Auth Far-left wouldn't be against the idea of old students teaching new students either.
Surveillance and Internet Security
Jeremy Corbyn was initially against the Government snooping around the in the General Public's Internet History and so on, but Corbyn Changed his Position to being in favour of the Investigatory Powers Act 2016 which was named by Edward Snowden to be "the most extreme surveillance in the history of western democracy. It goes further than many autocracies", I think a lot of you know what i'm going to say about this, This position isn't just Authoritarian but it's not even Left leaning at all. It is one of the most Conservative view points that Corbyn has (albeit he doesn't have that many).
Both The Libertarian and Authoritarian Far-left would be against such a bill. However, the Authoritarian far-left would have much more leniency towards it than the Libertarian Far-left would.
The EU/Brexit Stance
Corbyn himself was in favour of Brexit, no matter how much he loves to weasel word his way out of giving an actual answer on the question (Well done Corbyn, you are a real Politician now). However, in saying this, Corbyn does show some leniency on the idea of staying in the economic single market for some of the benefit of having consistent negotiable trade deals to keep the Economy afloat. Brexit isn't really a partisan issue per se, since there are good left wing reasons to leave the EU, such as workers rights being at risk, and not being put in the hands of the country itself, etc, etc. Most of those reasons Corbyn has in his weasel wording given some credit to, so he gets a point for that. Corbyn wasn't in favour of Brexit for "border control" unlike the right wing, it was purely for Economic and Worker's Rights issues, Immigration has never been an issue for Corbyn.
The Libertarian Far-left are against the EU, because there is something worrying about not just not having a large seat at the table in the EU to make decisions but having to rely on the rest of Europe to vote in "decent" politicians that will actually protect your individual liberties like medical cannabis and LGBT rights, as well as your right to strike.
The Authoritarian Far-left are also against the EU for almost identical reasoning to the Libertarian Far-left. Plus the whole speech about "Bringing all decision making into the hands of the Democratically Centralised Government".
Trade Unions
Jeremy Corbyn is in favour of Trade Unions and believes that for the most part that Trade Unions are a staple of a functioning Democracy as well as a protector of fundamental Worker's Rights. This is fundamentally a left wing staple of Politics, most of the rational behind the support of worker's rights can be found in Left wing thinkers like Karl Marx and Vladimir Lenin. However, some conservative countries do have trade union rights, they are just very strictly controlled. Controls that Corbyn is not in favour of at all.
Both the Authoritarian Far-Left and Libertarian Far-left Agree that Trade Unions should be a fundamental part of any society, not just because they can serve the workers but they can also protect a societies individual rights as well. Only major difference is that, with the authoritarian far-left, The trade unions would be dependent on the decisions of the state council, and with the Libertarian Far-left the trade unions would be free to impact the direct democracies as they exist in anyway that was appropriate.
Evaluation
Jeremy Corbyn is a breath of fresh air, not because he is far-left. He isn't at all, he is a breath of fresh air to the Labour party and Centre-left newspapers because they have spent years having to deal with the same Tony Blair inspired politicians including Ed Milliband and Gordon Brown. He shares some vaguely left wing views, but overall he is not far-left, he's not even moderately far-left. Jeremy Corbyn is a more Socially Liberal Social Democrat. Which in comparison to the pro-business "new labour" that labour has been plagued with since 1994, Corbyn is a Radical, just not a far-left radical.
Much of the hype around Jeremy Corbyn being a radical change to the Labour Party is not too dissimilar to the hype around Clement Attlee when he was named Leader of the Labour Party. Historically and view point wise, Attlee and Corbyn have quite a lot in common, and for what it is worth Corbyn although not Radical or Far-left, he is a sign that Labour might actually be going back to it's former glory, Let's hope it stays that way.