The A57(M) is better known as the famous Mancunian Way - an elevated road that has entered popular culture, forming a high-standard bypass for central Manchester. Much of it is up on stilts crossing over other streets.
There was a great deal of excitement in Manchester around its 1967 opening; the Manchester Evening News ran article after article on the 'highway in the sky', which was seen then as a major engineering feat and a very positive development for the city. In fact, when it first opened, the road wasn't quite long as it is now. The A56 and A6 junctions were both flat roundabouts back then, effectively marking the end of the road, and they were only grade-separated in the early 1990s.
Most of the A57(M)'s junctions are unusual and require care and attention, partly because the road was just plain-vanilla A57 when it opened, and motorway restrictions were added on later. Its speed limit was also raised from an initial 30 to the current 50 when it was realised that vehicles were capable of travelling on the road without falling off at this breakneck pace.
Popular wisdom is that the Brook Street junction with the A34 has a mistake: there is an unfinished sliproad leaving the eastbound carriageway to head north - though it ends in mid air because during construction it was abandoned when the contractors realised that it would carry traffic the wrong way onto a one way street. That's not true, of course, and nobody building a motorway like this would be daft enough to start pouring concrete before checking which way the traffic went on the streets nearby. In fact, there was a plan for Brook Street to be widened and become two-way at the time the road was built, which is a far more sensible explanation, if admittedly also less interesting.
The flyover across the A6 interchange at the motorway's eastern end is technically not the A57(M) at all - legal orders that apply motorway restrictions to it reveal that it's actually the A635(M), a secret number that doesn't appear on any signs. But for our purposes here, let's not be too picky - the world knows it as the Mancunian Way so there's little point quibbling about its number.